From d55fb1c73721686a652ffa02da1892900e74782d Mon Sep 17 00:00:00 2001 From: generall Date: Fri, 16 Aug 2024 01:51:27 +0200 Subject: [PATCH 1/8] add draft article --- qdrant-landing/content/articles/immutable.md | 135 +++++++++++++++++++ 1 file changed, 135 insertions(+) create mode 100644 qdrant-landing/content/articles/immutable.md diff --git a/qdrant-landing/content/articles/immutable.md b/qdrant-landing/content/articles/immutable.md new file mode 100644 index 000000000..2c2feabc0 --- /dev/null +++ b/qdrant-landing/content/articles/immutable.md @@ -0,0 +1,135 @@ +--- +title: "Qdrant internals: immutable data structures" +short_description: "How immutability helps Qdrant do vector search blazingly fast" +description: "How immutability helps Qdrant do vector search blazingly fast" +social_preview_image: /articles_data/immutable/social_preview.png +preview_dir: /articles_data/immutable/preview +weight: -200 +author: Andrey Vasnetsov +date: 2024-08-01T09:45:00+02:00 +draft: false +keywords: + - data structures + - optimization + - immutable data structures +--- + +## Data Structures 101 + +You know from your freshman year that there is no such thing as a universal data structure. +Some data structures are really good at providing access to elements by their index (like arrays), while others have a better insertion complexity (like linked lists). + +Everything becomes even more complicated when you start thinking about program execution in real harware. +Big-O notation suddenly becomes irrelevant, if you have to deal with cache misses, memory layout, and other low-level stuff. + +From the hardware perspective, the best data structure we can have is a simple contiguous array of bytes, which is being read sequentially in a single thread. +In this scenario all optimization mechanisms work perfectly: prefetching, caches, branch prediction and so on. + +The further we go from this ideal scenario, the more we have to pay for the complexity of our data structures. +And the complexity is the result of additional requirements we set for our data structures. + +### Mutability + +One of the most challenging requirements is ability to change the data structure after it was created. +Especially, if the update operation is supposed to be fast. + +Consider a simple example: we need want to have an ability to iterate over items in sorted order. +Without a mutability requirement, we can use a simple array and sort it once. +This is very close to our ideal scenario. We can even put the structure on disk - this is trivial for an array. + +But if we would want to insert an element into this array, we would have to shift all elements after the insertion point. +The time complexity of this operation is linear, and it is not acceptable for many applications. + +The alternative data structure, suitable for this task, is a B-tree. +Much more complex structure, which has to sacrifice efficiency of read operations to provide fast insertions. + +```rust +use std::collections::BTreeSet; +use rand::Rng; + +fn main() { + // Benchmark plain vector VS btree in a task of iteration over all elements + let mut rand = rand::thread_rng(); + let vector: Vec<_> = (0..1000000).map(|_| rand.gen::()).collect(); + let btree: BTreeSet<_> = vector.iter().copied().collect(); + + { + let mut sum = 0; + for el in vector { + sum += el; + } + } // Elapsed: 850.924µs + + { + let mut sum = 0; + for el in btree { + sum += el; + } + } // Elapsed: 5.213025ms, ~6x slower + +} +``` + +Vector Search engines, like Qdrant, have to deal with a large variety of data structures, but all of them have one thing in common: +if we could make them immutable, it could significantly help us to improve performance and optimize memory usage. + +## What immutability can improve exactly? + +Large part of immutable advantage comes from the fact, that we know the exact data we need to put into the structure even before we start building it. +Simplest example is a sorted array: we would know exactly how many elements we have to put into the array, so we can allocate exact amount of memory once. + +More complex data structures might require additional statistics to be collected before the structure is built. +Qdrant-related example of this is Scalar Quantization: on order to select proper quantization levels, we have to know the distribution of the data. + +(Image with quatiles here) + +Computing this distribution is requires knowing all the data in advance, but once we have it, applying scalar quantization is a simple operation. + +Let's take a look at non-exhaustive list of data structures and potential improvements we can get from making them immutable: + +|Function| Mutable Data Structure | Immutable Alternative | Potential improvements | +|----|------|------|------------------------| +| Read by index | Arrray | Fixed chunk of memory | Allocate exact amount of memory | +| Vector Storage | Array or Arrays | Memory-mapped file | Offload data to disk | +| Read sorted ranges| B-Tree | Sorted Array | Store all data close, avoid cache misses | +| Read by key | Hash Map | Hash Map with Perfect Hashing | Avoid hash collisions | +| Get documents by keyword | Inverted Index | Inverted Index with Sorted
and BitPacked Postings | Less memory usage, faster search | +| Vector Search | HNSW graph | HNSW graph with
paylaod-aware connections | Better precision with filters | +| Tenant isolation | Vector Storage | Defragmented Vector Storage | Faster access to on-disk data | + +About payload-aware connections in HNSW you can read in our [previous article](/articles/filtrable-hnsw/). + +But in this article I would like to describe a few of the latest additions to Qdrant: immutable hash map with perfect hashing and defragmented vector storage. + +### Perfect Hashing + +ToDo: Here describe how hash table with perfect hashing works and why it is important (see notion for details) + +### Deftagmentation + +ToDo + +* Describe why and when it is useful + * Disk is accessed by pages + * If page is bigger than vector, we waste cache + * If all relevant vectors for the tenant are together, we don't have cache misses even if vectors are small + +(Use image with defragmentation here) + + +## How to update immutable data structures? + +ToDo. + +Basically, two ideas: + +- Copy-on-write +- Soft-delete + +Also might we interesting to describe segments and how we can write to the segment, which is currently under optimization (and have to be read-only). + +## Downsides and how to compensate them + +* Immutable data structures are less efficient for updates, amortized complexity is the same, but constant factor is higher. Sometimes we need to build index twice for the same data. +* Immutable data structures assume read (search) heavy workload, which is expected for search engines. +* With segments it is possible to fallback to mutable data structures, so abitily to have immutable storage is more generic and flexible, than just mutable storage. From 65f1b6aa62cc82cdb2fef20a71dea7f043c2a7a5 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Tim=20Vis=C3=A9e?= Date: Fri, 16 Aug 2024 10:10:34 +0200 Subject: [PATCH 2/8] Fix some typos, sentences and punctuation --- qdrant-landing/content/articles/immutable.md | 30 ++++++++++---------- 1 file changed, 15 insertions(+), 15 deletions(-) diff --git a/qdrant-landing/content/articles/immutable.md b/qdrant-landing/content/articles/immutable.md index 2c2feabc0..be199fa28 100644 --- a/qdrant-landing/content/articles/immutable.md +++ b/qdrant-landing/content/articles/immutable.md @@ -19,7 +19,7 @@ keywords: You know from your freshman year that there is no such thing as a universal data structure. Some data structures are really good at providing access to elements by their index (like arrays), while others have a better insertion complexity (like linked lists). -Everything becomes even more complicated when you start thinking about program execution in real harware. +Everything becomes even more complicated when you start thinking about program execution in real hardware. Big-O notation suddenly becomes irrelevant, if you have to deal with cache misses, memory layout, and other low-level stuff. From the hardware perspective, the best data structure we can have is a simple contiguous array of bytes, which is being read sequentially in a single thread. @@ -30,10 +30,10 @@ And the complexity is the result of additional requirements we set for our data ### Mutability -One of the most challenging requirements is ability to change the data structure after it was created. +One of the most challenging requirements is the ability to change the data structure after it was created. Especially, if the update operation is supposed to be fast. -Consider a simple example: we need want to have an ability to iterate over items in sorted order. +Consider a simple example: we need to have an ability to iterate over items in sorted order. Without a mutability requirement, we can use a simple array and sort it once. This is very close to our ideal scenario. We can even put the structure on disk - this is trivial for an array. @@ -75,17 +75,17 @@ if we could make them immutable, it could significantly help us to improve perfo ## What immutability can improve exactly? -Large part of immutable advantage comes from the fact, that we know the exact data we need to put into the structure even before we start building it. -Simplest example is a sorted array: we would know exactly how many elements we have to put into the array, so we can allocate exact amount of memory once. +A large part of immutable advantage comes from the fact, that we know the exact data we need to put into the structure even before we start building it. +The simplest example is a sorted array: we would know exactly how many elements we have to put into the array, so we can allocate the exact amount of memory once. More complex data structures might require additional statistics to be collected before the structure is built. -Qdrant-related example of this is Scalar Quantization: on order to select proper quantization levels, we have to know the distribution of the data. +Qdrant-related example of this is Scalar Quantization: in order to select proper quantization levels, we have to know the distribution of the data. (Image with quatiles here) -Computing this distribution is requires knowing all the data in advance, but once we have it, applying scalar quantization is a simple operation. +Computing this distribution requires knowing all the data in advance, but once we have it, applying scalar quantization is a simple operation. -Let's take a look at non-exhaustive list of data structures and potential improvements we can get from making them immutable: +Let's take a look at a non-exhaustive list of data structures and potential improvements we can get from making them immutable: |Function| Mutable Data Structure | Immutable Alternative | Potential improvements | |----|------|------|------------------------| @@ -94,22 +94,22 @@ Let's take a look at non-exhaustive list of data structures and potential improv | Read sorted ranges| B-Tree | Sorted Array | Store all data close, avoid cache misses | | Read by key | Hash Map | Hash Map with Perfect Hashing | Avoid hash collisions | | Get documents by keyword | Inverted Index | Inverted Index with Sorted
and BitPacked Postings | Less memory usage, faster search | -| Vector Search | HNSW graph | HNSW graph with
paylaod-aware connections | Better precision with filters | +| Vector Search | HNSW graph | HNSW graph with
payload-aware connections | Better precision with filters | | Tenant isolation | Vector Storage | Defragmented Vector Storage | Faster access to on-disk data | About payload-aware connections in HNSW you can read in our [previous article](/articles/filtrable-hnsw/). -But in this article I would like to describe a few of the latest additions to Qdrant: immutable hash map with perfect hashing and defragmented vector storage. +But in this article, I would like to describe a few of the latest additions to Qdrant: immutable hash map with perfect hashing and defragmented vector storage. ### Perfect Hashing ToDo: Here describe how hash table with perfect hashing works and why it is important (see notion for details) -### Deftagmentation +### Defragmentation ToDo -* Describe why and when it is useful +* Describe how, why and when it is useful * Disk is accessed by pages * If page is bigger than vector, we waste cache * If all relevant vectors for the tenant are together, we don't have cache misses even if vectors are small @@ -126,10 +126,10 @@ Basically, two ideas: - Copy-on-write - Soft-delete -Also might we interesting to describe segments and how we can write to the segment, which is currently under optimization (and have to be read-only). +Also, it might be interesting to describe segments and how we can write to the segment, which is currently under optimization (and have to be read-only). ## Downsides and how to compensate them -* Immutable data structures are less efficient for updates, amortized complexity is the same, but constant factor is higher. Sometimes we need to build index twice for the same data. +* Immutable data structures are less efficient for updates, amortized complexity is the same, but constant factor is higher. Sometimes we need to build an index twice for the same data. * Immutable data structures assume read (search) heavy workload, which is expected for search engines. -* With segments it is possible to fallback to mutable data structures, so abitily to have immutable storage is more generic and flexible, than just mutable storage. +* With segments it is possible to fall back to mutable data structures, so ability to have immutable storage is more generic and flexible, than just mutable storage. From 982b5150971e880eb60667ecc1defd00b2309b70 Mon Sep 17 00:00:00 2001 From: davidmyriel Date: Mon, 19 Aug 2024 20:02:17 -0700 Subject: [PATCH 3/8] update text --- .../articles/immutable-data-structures.md | 160 ++++++++++++++++++ qdrant-landing/content/articles/immutable.md | 135 --------------- .../defragmentation.png | Bin 0 -> 90716 bytes 3 files changed, 160 insertions(+), 135 deletions(-) create mode 100644 qdrant-landing/content/articles/immutable-data-structures.md delete mode 100644 qdrant-landing/content/articles/immutable.md create mode 100644 qdrant-landing/static/articles_data/immutable-data-structures/defragmentation.png diff --git a/qdrant-landing/content/articles/immutable-data-structures.md b/qdrant-landing/content/articles/immutable-data-structures.md new file mode 100644 index 000000000..a802dc1a5 --- /dev/null +++ b/qdrant-landing/content/articles/immutable-data-structures.md @@ -0,0 +1,160 @@ +--- +title: "Immutable Data Structures for Superior Vector Search Performance" +short_description: "Learn how immutable data structures improve vector search performance in Qdrant." +description: "Learn about the advantages of immutability, perfect hashing and defragmentation. Our new approach carries great potential for large-scale search systems." +social_preview_image: /articles_data/immutable-data-structures/social_preview.png +preview_dir: /articles_data/immutable-data-structures/preview +weight: -200 +author: Andrey Vasnetsov +date: 2024-08-16T09:45:00+02:00 +draft: false +keywords: + - data structures + - optimization + - immutable data structures +--- + +## Does the Ideal Data Structure Exist? + +Those who took programming courses might remember that there is no such thing as a universal data structure. Some structures are excellent at accessing elements by index (like arrays), while others shine in terms of insertion efficiency (like linked lists). + +However, when we move from theoretical data structures to real-world systems, and particularly in performance-critical areas such as vector search, things become more complex. [Big-O notation](https://en.wikipedia.org/wiki/Big_O_notation) provides a good abstraction, but it doesn’t account for the realities of modern hardware: cache misses, memory layout, disk I/O, and other low-level considerations that influence actual performance. + +> From the perspective of hardware efficiency, the ideal data structure is a simple, contiguous array of bytes that can be read sequentially in a single thread. This scenario allows hardware optimizations like prefetching, caching, and branch prediction to operate at their best. + +However, real-world use cases require more complex structures to meet various operational needs, like mutability, efficient insertions, and indexing. These requirements increase complexity and introduce performance trade-offs, particularly in the case of mutability. + +### Mutability: Trading Performance for Flexibility + +One of the most significant challenges when working with data structures is ensuring mutability — the ability to change the data structure after it’s created, particularly with fast update operations. + +Let’s consider a simple example: we want to maintain a list of items that can be accessed in sorted order. Without mutability, we could simply use an array and sort it once, leading to very efficient reads. The array could even be memory-mapped to disk, making it highly space-efficient. + +However, if we need to insert an item into this array, **things get more complicated**. Inserting into a sorted array requires shifting all elements after the insertion point, which leads to linear time complexity for each insertion. This might be tolerable in memory, but it becomes problematic when dealing with disk-based storage. + +To handle such cases, more complex structures like [B-trees](https://en.wikipedia.org/wiki/B-tree) come into play. B-trees are specifically designed to optimize both insertion and read operations for large data sets, especially on disk. However, they sacrifice the raw speed of array reads for better insertion performance. + +Here’s a benchmark that illustrates the difference between a plain array and a B-tree in Rust.
This example shows that B-trees, although necessary for mutable sorted collections, **can significantly slow down read operations compared to arrays**. Therefore, we often aim to minimize mutability in search engines like Qdrant. + +```rust +use std::collections::BTreeSet; +use rand::Rng; + +fn main() { + // Benchmark plain vector VS btree in a task of iteration over all elements + let mut rand = rand::thread_rng(); + let vector: Vec<_> = (0..1000000).map(|_| rand.gen::()).collect(); + let btree: BTreeSet<_> = vector.iter().copied().collect(); + + { + let mut sum = 0; + for el in vector { + sum += el; + } + } // Elapsed: 850.924µs + + { + let mut sum = 0; + for el in btree { + sum += el; + } + } // Elapsed: 5.213025ms, ~6x slower + +} +``` + +## Why Immutability Helps + +Making data structures immutable can unlock significant performance optimizations, especially for read-heavy workloads like those in search engines. When a data structure is immutable, **you know the exact shape and size of the data in advance**, allowing you to optimize memory allocation and avoid costly update operations. + +Consider a sorted array, for example. When building the array immutably, we can allocate the exact amount of memory upfront and ensure that all data resides in contiguous memory. This avoids cache misses during reads and makes the structure highly efficient to traverse. + +Immutability also enables the use of advanced techniques like [memory-mapped files](https://en.wikipedia.org/wiki/Memory-mapped_file), where data can be stored on disk but treated as if it resides in memory. This makes large datasets manageable and ensures minimal memory usage. + +## Immutability in Qdrant: Scalar Quantization + +In Qdrant, one example of the benefits of immutability is the [scalar quantization](/articles/scalar-quantization/) technique. Scalar quantization is used to reduce the memory footprint of vector data by encoding it into a smaller representation. To apply this technique effectively, we need to know the distribution of the data upfront, which is only possible with immutable data. + +Here’s how it works: + +1. **Data distribution:** We collect dataset statistics: min, max, and distribution of vector magnitudes. +2. **Quantization levels:** Based on this distribution, we compute the optimal quantization levels. +3. **Encoding:** Once quantization levels are established, we apply them to the entire dataset. + +(Image with quatiles here) + +This is a computationally expensive process, but it only needs to be done once. + +> If the dataset were mutable, we would need to repeat this process with every update, drastically increasing overhead. + +## Immutability in Practice: Data Structure Improvements + +Here’s a more concrete look at how immutability improves specific data structures used in vector search engines: + +| Function | Mutable Data Structure | Immutable Alternative | Potential Improvements | +|---|---|---|---| +| **Read by index** | Dynamic Array | Static Array | Memory allocation can be optimized for read-heavy operations, avoiding overhead of resizing. | +| **Vector Storage** | Array of Arrays | Memory-mapped file | Memory offloading to disk saves RAM and improves cache performance. | +| **Read sorted ranges** | B-Tree | Sorted Array | Contiguous memory minimizes cache misses and improves read speed. | +| **Read by key** | Hash Map | Perfect Hash Map | Immutable hash maps can be optimized with **perfect hashing** to avoid collisions, improving lookup time. | +| **Keyword Search** | Inverted Index | Inverted Index with Bit-Packed Postings | Immutability allows efficient compression of index data, reducing memory footprint and boosting search speed. | +| **Vector Search** | HNSW Graph | HNSW Graph with Payload-Aware Connections | Immutable graph structures improve precision in filtered vector search. | +| **Tenant Isolation** | Fragmented Vector Storage | Defragmented Vector Storage | Placing vectors for a tenant contiguously reduces disk I/O and cache misses. | + +For more info on payload-aware connections in HNSW, read our [previous article](/articles/filtrable-hnsw/). + +This time around, we should focus on the latest additions to Qdrant: +- **the immutable hash map with perfect hashing** +- **defragmented vector storage**. + +### Key Techniques: Perfect Hashing and Defragmentation + +**Perfect Hashing:** This method allows us to create a hash function that maps keys to unique indices without collisions. This is extremely useful for search engines, where lookup speed is critical. With perfect hashing, we eliminate the overhead of handling collisions, making searches faster and more predictable. + +A hash table with perfect hashing is built in two steps: + +1. **First-level hashing:** We assign each key to a bucket using a standard hash function. +2. **Second-level hashing:** For each bucket, we create a secondary hash function that ensures no collisions within the bucket. + +This two-level hashing guarantees constant time complexity for lookups. + +**Defragmentation:** In large-scale systems like vector search engines, defragmentation becomes crucial when storing data on disk. Disk access is page-based, and when vectors are scattered across different pages, it leads to wasted space and cache inefficiencies. + +By defragmenting storage, we ensure that vectors belonging to the same tenant or query are stored contiguously. This reduces cache misses and ensures that disk pages are used efficiently. + +![defragmentation](/articles_data/immutable-data-structures/defragmentation.png) + +## Updating Immutable Data Structures + +Immutability raises a natural question: How do we handle updates? The two primary techniques are copy-on-write and soft-delete. + +### Copy-on-Write: + +With this method, rather than modifying the data structure directly, we create a new copy with the updated data. The downside is increased memory usage, but it avoids complex locking mechanisms and maintains immutability. + +### Soft-Delete: + +When removing data, rather than physically deleting it from the structure, we mark it as deleted. This allows for efficient handling of deletes while keeping the data structure immutable. + +**Also, it might be interesting to describe segments and how we can write to the segment, which is currently under optimization (and have to be read-only).** + +## Downsides and How to Compensate + +While immutable data structures are great for read-heavy operations, they come with trade-offs: + +- **Higher update costs:** Immutable structures are less efficient for updates. The amortized time complexity might be the same as mutable structures, but the constant factor is higher. +- **Rebuilding overhead:** In some cases, we may need to rebuild indices or structures for the same data more than once. +- **Read-heavy workloads:** Immutability assumes a search-heavy workload, which is typical for search engines but not for all applications. + +In Qdrant, we mitigate these downsides with a hybrid approach: segmenting data. Immutable structures handle the bulk of read operations, but we can fall back on mutable structures for data that is frequently updated. + +## Conclusion + +Immutable data structures, while tricky to implement correctly, offer significant performance gains, especially for read-heavy systems like search engines. They allow us to take full advantage of hardware optimizations, reduce memory overhead, and improve cache performance. + +In Qdrant, the combination of techniques like perfect hashing and defragmentation brings further benefits, making our vector search operations faster and more efficient. While there are trade-offs, the flexibility of Qdrant’s architecture — including segment-based storage — allows us to balance the best of both worlds. + + + + + diff --git a/qdrant-landing/content/articles/immutable.md b/qdrant-landing/content/articles/immutable.md deleted file mode 100644 index be199fa28..000000000 --- a/qdrant-landing/content/articles/immutable.md +++ /dev/null @@ -1,135 +0,0 @@ ---- -title: "Qdrant internals: immutable data structures" -short_description: "How immutability helps Qdrant do vector search blazingly fast" -description: "How immutability helps Qdrant do vector search blazingly fast" -social_preview_image: /articles_data/immutable/social_preview.png -preview_dir: /articles_data/immutable/preview -weight: -200 -author: Andrey Vasnetsov -date: 2024-08-01T09:45:00+02:00 -draft: false -keywords: - - data structures - - optimization - - immutable data structures ---- - -## Data Structures 101 - -You know from your freshman year that there is no such thing as a universal data structure. -Some data structures are really good at providing access to elements by their index (like arrays), while others have a better insertion complexity (like linked lists). - -Everything becomes even more complicated when you start thinking about program execution in real hardware. -Big-O notation suddenly becomes irrelevant, if you have to deal with cache misses, memory layout, and other low-level stuff. - -From the hardware perspective, the best data structure we can have is a simple contiguous array of bytes, which is being read sequentially in a single thread. -In this scenario all optimization mechanisms work perfectly: prefetching, caches, branch prediction and so on. - -The further we go from this ideal scenario, the more we have to pay for the complexity of our data structures. -And the complexity is the result of additional requirements we set for our data structures. - -### Mutability - -One of the most challenging requirements is the ability to change the data structure after it was created. -Especially, if the update operation is supposed to be fast. - -Consider a simple example: we need to have an ability to iterate over items in sorted order. -Without a mutability requirement, we can use a simple array and sort it once. -This is very close to our ideal scenario. We can even put the structure on disk - this is trivial for an array. - -But if we would want to insert an element into this array, we would have to shift all elements after the insertion point. -The time complexity of this operation is linear, and it is not acceptable for many applications. - -The alternative data structure, suitable for this task, is a B-tree. -Much more complex structure, which has to sacrifice efficiency of read operations to provide fast insertions. - -```rust -use std::collections::BTreeSet; -use rand::Rng; - -fn main() { - // Benchmark plain vector VS btree in a task of iteration over all elements - let mut rand = rand::thread_rng(); - let vector: Vec<_> = (0..1000000).map(|_| rand.gen::()).collect(); - let btree: BTreeSet<_> = vector.iter().copied().collect(); - - { - let mut sum = 0; - for el in vector { - sum += el; - } - } // Elapsed: 850.924µs - - { - let mut sum = 0; - for el in btree { - sum += el; - } - } // Elapsed: 5.213025ms, ~6x slower - -} -``` - -Vector Search engines, like Qdrant, have to deal with a large variety of data structures, but all of them have one thing in common: -if we could make them immutable, it could significantly help us to improve performance and optimize memory usage. - -## What immutability can improve exactly? - -A large part of immutable advantage comes from the fact, that we know the exact data we need to put into the structure even before we start building it. -The simplest example is a sorted array: we would know exactly how many elements we have to put into the array, so we can allocate the exact amount of memory once. - -More complex data structures might require additional statistics to be collected before the structure is built. -Qdrant-related example of this is Scalar Quantization: in order to select proper quantization levels, we have to know the distribution of the data. - -(Image with quatiles here) - -Computing this distribution requires knowing all the data in advance, but once we have it, applying scalar quantization is a simple operation. - -Let's take a look at a non-exhaustive list of data structures and potential improvements we can get from making them immutable: - -|Function| Mutable Data Structure | Immutable Alternative | Potential improvements | -|----|------|------|------------------------| -| Read by index | Arrray | Fixed chunk of memory | Allocate exact amount of memory | -| Vector Storage | Array or Arrays | Memory-mapped file | Offload data to disk | -| Read sorted ranges| B-Tree | Sorted Array | Store all data close, avoid cache misses | -| Read by key | Hash Map | Hash Map with Perfect Hashing | Avoid hash collisions | -| Get documents by keyword | Inverted Index | Inverted Index with Sorted
and BitPacked Postings | Less memory usage, faster search | -| Vector Search | HNSW graph | HNSW graph with
payload-aware connections | Better precision with filters | -| Tenant isolation | Vector Storage | Defragmented Vector Storage | Faster access to on-disk data | - -About payload-aware connections in HNSW you can read in our [previous article](/articles/filtrable-hnsw/). - -But in this article, I would like to describe a few of the latest additions to Qdrant: immutable hash map with perfect hashing and defragmented vector storage. - -### Perfect Hashing - -ToDo: Here describe how hash table with perfect hashing works and why it is important (see notion for details) - -### Defragmentation - -ToDo - -* Describe how, why and when it is useful - * Disk is accessed by pages - * If page is bigger than vector, we waste cache - * If all relevant vectors for the tenant are together, we don't have cache misses even if vectors are small - -(Use image with defragmentation here) - - -## How to update immutable data structures? - -ToDo. - -Basically, two ideas: - -- Copy-on-write -- Soft-delete - -Also, it might be interesting to describe segments and how we can write to the segment, which is currently under optimization (and have to be read-only). - -## Downsides and how to compensate them - -* Immutable data structures are less efficient for updates, amortized complexity is the same, but constant factor is higher. 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Date: Tue, 20 Aug 2024 12:57:06 +0200 Subject: [PATCH 4/8] rollback text changes --- .../articles/immutable-data-structures.md | 106 ++++++++---------- 1 file changed, 49 insertions(+), 57 deletions(-) diff --git a/qdrant-landing/content/articles/immutable-data-structures.md b/qdrant-landing/content/articles/immutable-data-structures.md index a802dc1a5..45da79b84 100644 --- a/qdrant-landing/content/articles/immutable-data-structures.md +++ b/qdrant-landing/content/articles/immutable-data-structures.md @@ -14,27 +14,32 @@ keywords: - immutable data structures --- -## Does the Ideal Data Structure Exist? +## Data Structures 101 -Those who took programming courses might remember that there is no such thing as a universal data structure. Some structures are excellent at accessing elements by index (like arrays), while others shine in terms of insertion efficiency (like linked lists). +Those who took programming courses might remember that there is no such thing as a universal data structure. +Some structures are good at accessing elements by index (like arrays), while others shine in terms of insertion efficiency (like linked lists). However, when we move from theoretical data structures to real-world systems, and particularly in performance-critical areas such as vector search, things become more complex. [Big-O notation](https://en.wikipedia.org/wiki/Big_O_notation) provides a good abstraction, but it doesn’t account for the realities of modern hardware: cache misses, memory layout, disk I/O, and other low-level considerations that influence actual performance. -> From the perspective of hardware efficiency, the ideal data structure is a simple, contiguous array of bytes that can be read sequentially in a single thread. This scenario allows hardware optimizations like prefetching, caching, and branch prediction to operate at their best. +> From the perspective of hardware efficiency, the ideal data structure is a contiguous array of bytes that can be read sequentially in a single thread. This scenario allows hardware optimizations like prefetching, caching, and branch prediction to operate at their best. -However, real-world use cases require more complex structures to meet various operational needs, like mutability, efficient insertions, and indexing. These requirements increase complexity and introduce performance trade-offs, particularly in the case of mutability. +However, real-world use cases require more complex structures to perform varios operations like insertion, deletion, and search. +These requirements increase complexity and introduce performance trade-offs. -### Mutability: Trading Performance for Flexibility +### Mutability One of the most significant challenges when working with data structures is ensuring mutability — the ability to change the data structure after it’s created, particularly with fast update operations. -Let’s consider a simple example: we want to maintain a list of items that can be accessed in sorted order. Without mutability, we could simply use an array and sort it once, leading to very efficient reads. The array could even be memory-mapped to disk, making it highly space-efficient. +Let’s consider a simple example: we want to iterate over items in sorted order. +Without a mutability requirement, we can use a simple array and sort it once. +This is very close to our ideal scenario. We can even put the structure on disk - this is trivial for an array. -However, if we need to insert an item into this array, **things get more complicated**. Inserting into a sorted array requires shifting all elements after the insertion point, which leads to linear time complexity for each insertion. This might be tolerable in memory, but it becomes problematic when dealing with disk-based storage. +However, if we need to insert an item into this array, **things get more complicated**. +Inserting into a sorted array requires shifting all elements after the insertion point, which leads to linear time complexity for each insertion, which is not acceptable for many applications. -To handle such cases, more complex structures like [B-trees](https://en.wikipedia.org/wiki/B-tree) come into play. B-trees are specifically designed to optimize both insertion and read operations for large data sets, especially on disk. However, they sacrifice the raw speed of array reads for better insertion performance. +To handle such cases, more complex structures like [B-trees](https://en.wikipedia.org/wiki/B-tree) come into play. B-trees are specifically designed to optimize both insertion and read operations for large data sets. However, they sacrifice the raw speed of array reads for better insertion performance. -Here’s a benchmark that illustrates the difference between a plain array and a B-tree in Rust.
This example shows that B-trees, although necessary for mutable sorted collections, **can significantly slow down read operations compared to arrays**. Therefore, we often aim to minimize mutability in search engines like Qdrant. +Here’s a benchmark that illustrates the difference between iterating over a plain array and a BTreeSet in Rust: ```rust use std::collections::BTreeSet; @@ -63,80 +68,64 @@ fn main() { } ``` -## Why Immutability Helps +Vector Search engines, like Qdrant, have to deal with a large variety of data structures. +If we could make them immutable, it would significantly improve performance and optimize memory usage. -Making data structures immutable can unlock significant performance optimizations, especially for read-heavy workloads like those in search engines. When a data structure is immutable, **you know the exact shape and size of the data in advance**, allowing you to optimize memory allocation and avoid costly update operations. +## What immutability can improve exactly? -Consider a sorted array, for example. When building the array immutably, we can allocate the exact amount of memory upfront and ensure that all data resides in contiguous memory. This avoids cache misses during reads and makes the structure highly efficient to traverse. +A large part of the immutable advantage comes from the fact that we know the exact data we need to put into the structure even before we start building it. +The simplest example is a sorted array: we would know exactly how many elements we have to put into the array so we can allocate the exact amount of memory once. -Immutability also enables the use of advanced techniques like [memory-mapped files](https://en.wikipedia.org/wiki/Memory-mapped_file), where data can be stored on disk but treated as if it resides in memory. This makes large datasets manageable and ensures minimal memory usage. - -## Immutability in Qdrant: Scalar Quantization - -In Qdrant, one example of the benefits of immutability is the [scalar quantization](/articles/scalar-quantization/) technique. Scalar quantization is used to reduce the memory footprint of vector data by encoding it into a smaller representation. To apply this technique effectively, we need to know the distribution of the data upfront, which is only possible with immutable data. - -Here’s how it works: - -1. **Data distribution:** We collect dataset statistics: min, max, and distribution of vector magnitudes. -2. **Quantization levels:** Based on this distribution, we compute the optimal quantization levels. -3. **Encoding:** Once quantization levels are established, we apply them to the entire dataset. +More complex data structures might require additional statistics to be collected before the structure is built. +A qdrant-related example of this is Scalar Quantization: in order to select proper quantization levels, we have to know the distribution of the data. (Image with quatiles here) -This is a computationally expensive process, but it only needs to be done once. +Computing this distribution requires knowing all the data in advance, but once we have it, applying scalar quantization is a simple operation. -> If the dataset were mutable, we would need to repeat this process with every update, drastically increasing overhead. +Let's take a look at a non-exhaustive list of data structures and potential improvements we can get from making them immutable: -## Immutability in Practice: Data Structure Improvements +|Function| Mutable Data Structure | Immutable Alternative | Potential improvements | +|----|------|------|------------------------| +| Read by index | Arrray | Fixed chunk of memory | Allocate exact amount of memory | +| Vector Storage | Array or Arrays | Memory-mapped file | Offload data to disk | +| Read sorted ranges| B-Tree | Sorted Array | Store all data close, avoid cache misses | +| Read by key | Hash Map | Hash Map with Perfect Hashing | Avoid hash collisions | +| Get documents by keyword | Inverted Index | Inverted Index with Sorted
and BitPacked Postings | Less memory usage, faster search | +| Vector Search | HNSW graph | HNSW graph with
payload-aware connections | Better precision with filters | +| Tenant Isolation | Vector Storage | Defragmented Vector Storage | Faster access to on-disk data | -Here’s a more concrete look at how immutability improves specific data structures used in vector search engines: - -| Function | Mutable Data Structure | Immutable Alternative | Potential Improvements | -|---|---|---|---| -| **Read by index** | Dynamic Array | Static Array | Memory allocation can be optimized for read-heavy operations, avoiding overhead of resizing. | -| **Vector Storage** | Array of Arrays | Memory-mapped file | Memory offloading to disk saves RAM and improves cache performance. | -| **Read sorted ranges** | B-Tree | Sorted Array | Contiguous memory minimizes cache misses and improves read speed. | -| **Read by key** | Hash Map | Perfect Hash Map | Immutable hash maps can be optimized with **perfect hashing** to avoid collisions, improving lookup time. | -| **Keyword Search** | Inverted Index | Inverted Index with Bit-Packed Postings | Immutability allows efficient compression of index data, reducing memory footprint and boosting search speed. | -| **Vector Search** | HNSW Graph | HNSW Graph with Payload-Aware Connections | Immutable graph structures improve precision in filtered vector search. | -| **Tenant Isolation** | Fragmented Vector Storage | Defragmented Vector Storage | Placing vectors for a tenant contiguously reduces disk I/O and cache misses. | For more info on payload-aware connections in HNSW, read our [previous article](/articles/filtrable-hnsw/). -This time around, we should focus on the latest additions to Qdrant: +This time around, we will focus on the latest additions to Qdrant: - **the immutable hash map with perfect hashing** - **defragmented vector storage**. -### Key Techniques: Perfect Hashing and Defragmentation +### Perfect Hashing -**Perfect Hashing:** This method allows us to create a hash function that maps keys to unique indices without collisions. This is extremely useful for search engines, where lookup speed is critical. With perfect hashing, we eliminate the overhead of handling collisions, making searches faster and more predictable. +ToDo: Here describe how hash table with perfect hashing works and why it is important (see notion for details) -A hash table with perfect hashing is built in two steps: -1. **First-level hashing:** We assign each key to a bucket using a standard hash function. -2. **Second-level hashing:** For each bucket, we create a secondary hash function that ensures no collisions within the bucket. +### Defragmentation -This two-level hashing guarantees constant time complexity for lookups. - -**Defragmentation:** In large-scale systems like vector search engines, defragmentation becomes crucial when storing data on disk. Disk access is page-based, and when vectors are scattered across different pages, it leads to wasted space and cache inefficiencies. - -By defragmenting storage, we ensure that vectors belonging to the same tenant or query are stored contiguously. This reduces cache misses and ensures that disk pages are used efficiently. +* Describe how, why and when it is useful + * Disk is accessed by pages + * If page is bigger than vector, we waste cache + * If all relevant vectors for the tenant are together, we don't have cache misses even if vectors are small ![defragmentation](/articles_data/immutable-data-structures/defragmentation.png) ## Updating Immutable Data Structures -Immutability raises a natural question: How do we handle updates? The two primary techniques are copy-on-write and soft-delete. +ToDo. -### Copy-on-Write: +Basically, two ideas: -With this method, rather than modifying the data structure directly, we create a new copy with the updated data. The downside is increased memory usage, but it avoids complex locking mechanisms and maintains immutability. +- Copy-on-write +- Soft-delete -### Soft-Delete: - -When removing data, rather than physically deleting it from the structure, we mark it as deleted. This allows for efficient handling of deletes while keeping the data structure immutable. - -**Also, it might be interesting to describe segments and how we can write to the segment, which is currently under optimization (and have to be read-only).** +Also, it might be interesting to describe segments and how we can write to the segment, which is currently under optimization (and have to be read-only). ## Downsides and How to Compensate @@ -146,7 +135,10 @@ While immutable data structures are great for read-heavy operations, they come w - **Rebuilding overhead:** In some cases, we may need to rebuild indices or structures for the same data more than once. - **Read-heavy workloads:** Immutability assumes a search-heavy workload, which is typical for search engines but not for all applications. -In Qdrant, we mitigate these downsides with a hybrid approach: segmenting data. Immutable structures handle the bulk of read operations, but we can fall back on mutable structures for data that is frequently updated. +In Qdrant, we mitigate these downsides by allowing the user to adapt the system to their specific workload. +For example, changing the default size of the segment might help to reduce the overhead of rebuilding indices. + +In extreme cases, multi-segment storage can act as a single segment, falling back to the mutable data structure when needed. ## Conclusion From 04df1374eacd5269fd64e6d1bae3f8b0b3b7c4ee Mon Sep 17 00:00:00 2001 From: generall Date: Tue, 20 Aug 2024 18:51:47 +0200 Subject: [PATCH 5/8] finish the article --- .../articles/immutable-data-structures.md | 126 +++++++++++++++--- .../hardware-optimized.png | Bin 0 -> 14706 bytes .../optimization.png | Bin 0 -> 55240 bytes .../immutable-data-structures/page-vector.png | Bin 0 -> 13694 bytes .../immutable-data-structures/preview.png | Bin 0 -> 1661829 bytes .../preview/preview.jpg | Bin 0 -> 31816 bytes .../preview/preview.webp | Bin 0 -> 28376 bytes .../preview/social_preview.jpg | Bin 0 -> 213666 bytes .../preview/title.jpg | Bin 0 -> 97097 bytes .../preview/title.webp | Bin 0 -> 86964 bytes .../quantization-quantile.png | Bin 0 -> 15032 bytes .../social_preview.png | Bin 0 -> 1011694 bytes 12 files changed, 106 insertions(+), 20 deletions(-) create mode 100644 qdrant-landing/static/articles_data/immutable-data-structures/hardware-optimized.png create mode 100644 qdrant-landing/static/articles_data/immutable-data-structures/optimization.png create mode 100644 qdrant-landing/static/articles_data/immutable-data-structures/page-vector.png create mode 100644 qdrant-landing/static/articles_data/immutable-data-structures/preview.png create mode 100644 qdrant-landing/static/articles_data/immutable-data-structures/preview/preview.jpg create mode 100644 qdrant-landing/static/articles_data/immutable-data-structures/preview/preview.webp create mode 100644 qdrant-landing/static/articles_data/immutable-data-structures/preview/social_preview.jpg create mode 100644 qdrant-landing/static/articles_data/immutable-data-structures/preview/title.jpg create mode 100644 qdrant-landing/static/articles_data/immutable-data-structures/preview/title.webp create mode 100644 qdrant-landing/static/articles_data/immutable-data-structures/quantization-quantile.png create mode 100644 qdrant-landing/static/articles_data/immutable-data-structures/social_preview.png diff --git a/qdrant-landing/content/articles/immutable-data-structures.md b/qdrant-landing/content/articles/immutable-data-structures.md index 45da79b84..9ca7d2621 100644 --- a/qdrant-landing/content/articles/immutable-data-structures.md +++ b/qdrant-landing/content/articles/immutable-data-structures.md @@ -1,17 +1,19 @@ --- -title: "Immutable Data Structures for Superior Vector Search Performance" +title: "Qdrant Internals: Immutable Data Structures" short_description: "Learn how immutable data structures improve vector search performance in Qdrant." -description: "Learn about the advantages of immutability, perfect hashing and defragmentation. Our new approach carries great potential for large-scale search systems." +description: "Learn how immutable data structures improve vector search performance in Qdrant." social_preview_image: /articles_data/immutable-data-structures/social_preview.png preview_dir: /articles_data/immutable-data-structures/preview weight: -200 author: Andrey Vasnetsov -date: 2024-08-16T09:45:00+02:00 +date: 2024-08-20T10:45:00+02:00 draft: false keywords: - data structures - optimization - immutable data structures + - perfect hashing + - defragmentation --- ## Data Structures 101 @@ -19,10 +21,13 @@ keywords: Those who took programming courses might remember that there is no such thing as a universal data structure. Some structures are good at accessing elements by index (like arrays), while others shine in terms of insertion efficiency (like linked lists). +{{< figure src="/articles_data/immutable-data-structures/hardware-optimized.png" alt="Hardware-optimized data structure" caption="Hardware-optimized data structure" width="80%" >}} + However, when we move from theoretical data structures to real-world systems, and particularly in performance-critical areas such as vector search, things become more complex. [Big-O notation](https://en.wikipedia.org/wiki/Big_O_notation) provides a good abstraction, but it doesn’t account for the realities of modern hardware: cache misses, memory layout, disk I/O, and other low-level considerations that influence actual performance. > From the perspective of hardware efficiency, the ideal data structure is a contiguous array of bytes that can be read sequentially in a single thread. This scenario allows hardware optimizations like prefetching, caching, and branch prediction to operate at their best. + However, real-world use cases require more complex structures to perform varios operations like insertion, deletion, and search. These requirements increase complexity and introduce performance trade-offs. @@ -77,9 +82,10 @@ A large part of the immutable advantage comes from the fact that we know the exa The simplest example is a sorted array: we would know exactly how many elements we have to put into the array so we can allocate the exact amount of memory once. More complex data structures might require additional statistics to be collected before the structure is built. -A qdrant-related example of this is Scalar Quantization: in order to select proper quantization levels, we have to know the distribution of the data. +A qdrant-related example of this is [Scalar Quantization](/articles/scalar-quantization/#conversion-to-integers): in order to select proper quantization levels, we have to know the distribution of the data. + +{{< figure src="/articles_data/immutable-data-structures/quantization-quantile.png" alt="Scalar Quantization Quantile" caption="Scalar Quantization Quantile" width="70%" >}} -(Image with quatiles here) Computing this distribution requires knowing all the data in advance, but once we have it, applying scalar quantization is a simple operation. @@ -104,28 +110,112 @@ This time around, we will focus on the latest additions to Qdrant: ### Perfect Hashing -ToDo: Here describe how hash table with perfect hashing works and why it is important (see notion for details) +Hash Table is one of the most commonly used data structures implemented in almost every programming language, including Rust. +They provide fast access to elements by key, with an average time complexity of O(1) for read and write operations. +There is, however, an assumption that should be satisfied for the hash table to work efficiently: *hash collisions should not cause too much overhead*. + +In regular mutable hash tables, this might be achieved by multiple strategies: + +* making the hash table bigger so the probability of collision is lower +* using a linked list or a tree to store multiple elements with the same hash + +However, these strategies have overheads, which become more significant if we consider using high-latency storage like disk. + +Indeed, every read operation from disk is order of magnitude slower than reading from RAM, so we want to know the correct location of the data from the first attempt. + +In order to achieve this, we can use a so-called perfect hash function(PHF). +A special type of hash function, constructed specifically for a given set of keys, guarantees no collisions while using minimal memory. + +In Qdrant, we decided to use *fingerprint-based minimal perfect hash function* implemented in the [ph create](https://crates.io/crates/ph) by [Piotr Beling](https://dl.acm.org/doi/10.1145/3596453). +According to our benchmarks, using the perfect hash function does introduce some overhead in terms of hashing time, but it significantly reduces the time for the whole operation: + +| Volume | `ph::Function` | `std::hash::Hash` | `HashMap::get`| +|--------|----------------|-------------------|---------------| +| 1000 | 60ns | ~20ns | 34ns | +| 100k | 90ns | ~20ns | 220ns | +| 10M | 238ns | ~20ns | 500ns | + +Even thought the absolute time for hasing is higher, the time for the whole operation is lower, because PHF guarantees no collisions. +The difference is even more significant when we consider the disk read time, which +might up to several milliseconds (10^6 ns). + +PHF RAM size scales linearly for `ph::Function`: 3.46 kB for 10k elements, 119MB for 350M elements. +And construction time requires to build the hash function is surprisingly low: (we only need to do it once): + +| Volume | `ph::Function` (construct) | PHF size | +|--------|----------------------------|----------| +| 1M | 52ms | 0.34Mb | +| 100M | 7.4s | 33.7Mb | + +Usage of PHF in Qdrant allows us to minimize latency of cold reads, which is especially important for large-scale multi-tenant systems. +With PHF, it is enough to read a single page from a disk to get the exact location of the data. ### Defragmentation -* Describe how, why and when it is useful - * Disk is accessed by pages - * If page is bigger than vector, we waste cache - * If all relevant vectors for the tenant are together, we don't have cache misses even if vectors are small +When you read data from a disk, you almost never read a single byte. Instead, you read a page, which is a fixed-size chunk of data. +On many systems, the page size is 4KB, which means that every read operation will read 4KB of data, even if you only need a single byte. + +Vector Search, on the other hand, requires reading a lot of small vectors, which might create a large overhead. +It is especially noticeable if we use binary quantization, where the size of even large OpenAI 1536d vectors is compressed down to **192 bytes**. + +{{< figure src="/articles_data/immutable-data-structures/page-vector.png" alt="Overhead when reading single vector" caption="Overhead when reading single vector" width="80%" >}} + +That means if the vectors we access during the search are randomly scattered across the disk, we will have to read 4KB for each vector, which is 20 times more than the actual data size. + +There is, however, a simple way to avoid this overhead: **defragmentation**. +If we knew some additional information about the data, we could combine all relevant vectors into a single page. + +{{< figure src="/articles_data/immutable-data-structures/defragmentation.png" alt="Defragmentation" caption="Defragmentation" width="70%" >}} + +This additional information is available to Qdrant via the payload index. + +By specifying the payload index, which is going to be used for filtering most of the time, we can put all vectors with the same payload together. +This way, reading a single page will also read nearby vectors, which will be used in the search. + +This approach is especially efficient for multi-tenant systems, where only a small subset of vectors is actively used for search. +Capacity of such deployment is typically defined by the size of hot subset, which is much smaller than the total number of vectors. + +Grouping relevant vectors together allows us to optimize the size of the hot subset by avoiding caching of irrelevant data. +Here are some benchmark data we have for comparing defragmented and non-defragmented storage: + +| % of hot subset | Tenant Size (vectors) | RPS, Non-defragmented | RPS, Defragmented | +|-----------------|-----------------------|-----------------------|-------------------| +| 2.5% | 50k | 1.5 | 304 | +| 12.5% | 50k | 0.47 | 279 | +| 25% | 50k | 0.4 | 63 | +| 50% | 50k | 0.3 | 8 | +| 2.5% | 5k | 56 | 490 | +| 12.5% | 5k | 5.8 | 488 | +| 25% | 5k | 3.3 | 490 | +| 50% | 5k | 3.1 | 480 | +| 75% | 5k | 2.9 | 130 | +| 100% | 5k | 2.7 | 95 | + + +Dataset size: 2M 768d vectors (~6Gb Raw data), binary quantization, 650Mb of RAM limit. +All benchmarks are made with minimal RAM allocation to demonstrate disk cache efficiency. + +As you can see, the biggest impact is on the small tenant size, where defragmentation allows us to achieve **100x more RPS**. +Of course, the real-world impact of defragmentation depends on the specific workload and the size of the hot subset, but enabling this feature can significantly improve the performance of Qdrant. + +Please find more details on how to enable defragmentation in the [index documentation](/documentation/concepts/indexing/#tenant-index). -![defragmentation](/articles_data/immutable-data-structures/defragmentation.png) ## Updating Immutable Data Structures -ToDo. +One may wonder how Qdrant allows updating collection data if everything is immutable. +Indeed, Qdrant API allows the change of any vector or payload at any time, so from the user's perspective, the whole collection is mutable at any time. -Basically, two ideas: +As it usually happens with every decent magic trick, the secret is disappointingly simple: not all data in Qdrant is immutable. +In Qdrant, we storage is divided into segments, which might be either mutable or immutable. +New data is always written to the mutable segment, which is later converted to the immutable one by the optimization process. -- Copy-on-write -- Soft-delete +{{< figure src="/articles_data/immutable-data-structures/optimization.png" alt="Optimization process" caption="Optimization process" width="80%" >}} -Also, it might be interesting to describe segments and how we can write to the segment, which is currently under optimization (and have to be read-only). +If we need to update the data in the immutable or currenly optimized segment, instead of changing the data in place, we perform a copy-on-write operation, move the data to the mutable segment, and update it there. + +Data in the original segment is marked as deleted, and later vacuumed by the optimization process. ## Downsides and How to Compensate @@ -146,7 +236,3 @@ Immutable data structures, while tricky to implement correctly, offer significan In Qdrant, the combination of techniques like perfect hashing and defragmentation brings further benefits, making our vector search operations faster and more efficient. 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a/qdrant-landing/content/articles/immutable-data-structures.md +++ b/qdrant-landing/content/articles/immutable-data-structures.md @@ -76,7 +76,7 @@ fn main() { Vector Search engines, like Qdrant, have to deal with a large variety of data structures. If we could make them immutable, it would significantly improve performance and optimize memory usage. -## What immutability can improve exactly? +## What exactly can immutability improve? A large part of the immutable advantage comes from the fact that we know the exact data we need to put into the structure even before we start building it. The simplest example is a sorted array: we would know exactly how many elements we have to put into the array so we can allocate the exact amount of memory once. From c5b59f99a7884c8dc17534bff47db9630c00fdce Mon Sep 17 00:00:00 2001 From: generall Date: Tue, 20 Aug 2024 19:05:22 +0200 Subject: [PATCH 7/8] review fix --- qdrant-landing/content/articles/immutable-data-structures.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/qdrant-landing/content/articles/immutable-data-structures.md b/qdrant-landing/content/articles/immutable-data-structures.md index 105b9e427..48d0fb96b 100644 --- a/qdrant-landing/content/articles/immutable-data-structures.md +++ b/qdrant-landing/content/articles/immutable-data-structures.md @@ -93,7 +93,7 @@ Let's take a look at a non-exhaustive list of data structures and potential impr |Function| Mutable Data Structure | Immutable Alternative | Potential improvements | |----|------|------|------------------------| -| Read by index | Arrray | Fixed chunk of memory | Allocate exact amount of memory | +| Read by index | Array | Fixed chunk of memory | Allocate exact amount of memory | | Vector Storage | Array or Arrays | Memory-mapped file | Offload data to disk | | Read sorted ranges| B-Tree | Sorted Array | Store all data close, avoid cache misses | | Read by key | Hash Map | Hash Map with Perfect Hashing | Avoid hash collisions | From 7bb2935837c73b0f58438cb1173452c1c9f54d40 Mon Sep 17 00:00:00 2001 From: davidmyriel Date: Tue, 20 Aug 2024 10:57:10 -0700 Subject: [PATCH 8/8] fix language and links --- .../articles/immutable-data-structures.md | 48 +++++++++---------- 1 file changed, 23 insertions(+), 25 deletions(-) diff --git a/qdrant-landing/content/articles/immutable-data-structures.md b/qdrant-landing/content/articles/immutable-data-structures.md index 48d0fb96b..24aef69d2 100644 --- a/qdrant-landing/content/articles/immutable-data-structures.md +++ b/qdrant-landing/content/articles/immutable-data-structures.md @@ -23,21 +23,20 @@ Some structures are good at accessing elements by index (like arrays), while oth {{< figure src="/articles_data/immutable-data-structures/hardware-optimized.png" alt="Hardware-optimized data structure" caption="Hardware-optimized data structure" width="80%" >}} -However, when we move from theoretical data structures to real-world systems, and particularly in performance-critical areas such as vector search, things become more complex. [Big-O notation](https://en.wikipedia.org/wiki/Big_O_notation) provides a good abstraction, but it doesn’t account for the realities of modern hardware: cache misses, memory layout, disk I/O, and other low-level considerations that influence actual performance. +However, when we move from theoretical data structures to real-world systems, and particularly in performance-critical areas such as [vector search](/use-cases/), things become more complex. [Big-O notation](https://en.wikipedia.org/wiki/Big_O_notation) provides a good abstraction, but it doesn’t account for the realities of modern hardware: cache misses, memory layout, disk I/O, and other low-level considerations that influence actual performance. > From the perspective of hardware efficiency, the ideal data structure is a contiguous array of bytes that can be read sequentially in a single thread. This scenario allows hardware optimizations like prefetching, caching, and branch prediction to operate at their best. - However, real-world use cases require more complex structures to perform varios operations like insertion, deletion, and search. These requirements increase complexity and introduce performance trade-offs. ### Mutability -One of the most significant challenges when working with data structures is ensuring mutability — the ability to change the data structure after it’s created, particularly with fast update operations. +One of the most significant challenges when working with data structures is ensuring **mutability — the ability to change the data structure after it’s created**, particularly with fast update operations. Let’s consider a simple example: we want to iterate over items in sorted order. Without a mutability requirement, we can use a simple array and sort it once. -This is very close to our ideal scenario. We can even put the structure on disk - this is trivial for an array. +This is very close to our ideal scenario. We can even put the structure on disk - which is trivial for an array. However, if we need to insert an item into this array, **things get more complicated**. Inserting into a sorted array requires shifting all elements after the insertion point, which leads to linear time complexity for each insertion, which is not acceptable for many applications. @@ -73,16 +72,16 @@ fn main() { } ``` -Vector Search engines, like Qdrant, have to deal with a large variety of data structures. +[Vector databases](https://qdrant.tech/), like Qdrant, have to deal with a large variety of data structures. If we could make them immutable, it would significantly improve performance and optimize memory usage. -## What exactly can immutability improve? +## How Does Immutability Help? A large part of the immutable advantage comes from the fact that we know the exact data we need to put into the structure even before we start building it. The simplest example is a sorted array: we would know exactly how many elements we have to put into the array so we can allocate the exact amount of memory once. More complex data structures might require additional statistics to be collected before the structure is built. -A qdrant-related example of this is [Scalar Quantization](/articles/scalar-quantization/#conversion-to-integers): in order to select proper quantization levels, we have to know the distribution of the data. +A Qdrant-related example of this is [Scalar Quantization](/articles/scalar-quantization/#conversion-to-integers): in order to select proper quantization levels, we have to know the distribution of the data. {{< figure src="/articles_data/immutable-data-structures/quantization-quantile.png" alt="Scalar Quantization Quantile" caption="Scalar Quantization Quantile" width="70%" >}} @@ -110,10 +109,10 @@ This time around, we will focus on the latest additions to Qdrant: ### Perfect Hashing -Hash Table is one of the most commonly used data structures implemented in almost every programming language, including Rust. -They provide fast access to elements by key, with an average time complexity of O(1) for read and write operations. +A hash table is one of the most commonly used data structures implemented in almost every programming language, including Rust. +It provides fast access to elements by key, with an average time complexity of O(1) for read and write operations. -There is, however, an assumption that should be satisfied for the hash table to work efficiently: *hash collisions should not cause too much overhead*. +There is, however, the assumption that should be satisfied for the hash table to work efficiently: *hash collisions should not cause too much overhead*. In regular mutable hash tables, this might be achieved by multiple strategies: @@ -124,8 +123,8 @@ However, these strategies have overheads, which become more significant if we co Indeed, every read operation from disk is order of magnitude slower than reading from RAM, so we want to know the correct location of the data from the first attempt. -In order to achieve this, we can use a so-called perfect hash function(PHF). -A special type of hash function, constructed specifically for a given set of keys, guarantees no collisions while using minimal memory. +In order to achieve this, we can use a so-called perfect hash function (PHF). +This a special type of hash function is constructed specifically for a given set of keys, and it guarantees no collisions while using minimal memory. In Qdrant, we decided to use *fingerprint-based minimal perfect hash function* implemented in the [ph create](https://crates.io/crates/ph) by [Piotr Beling](https://dl.acm.org/doi/10.1145/3596453). According to our benchmarks, using the perfect hash function does introduce some overhead in terms of hashing time, but it significantly reduces the time for the whole operation: @@ -136,27 +135,26 @@ According to our benchmarks, using the perfect hash function does introduce some | 100k | 90ns | ~20ns | 220ns | | 10M | 238ns | ~20ns | 500ns | -Even thought the absolute time for hasing is higher, the time for the whole operation is lower, because PHF guarantees no collisions. -The difference is even more significant when we consider the disk read time, which +Even thought the absolute time for hashing is higher, the time for the whole operation is lower, because PHF guarantees no collisions. +The difference is even more significant when we consider disk read time, which might up to several milliseconds (10^6 ns). PHF RAM size scales linearly for `ph::Function`: 3.46 kB for 10k elements, 119MB for 350M elements. -And construction time requires to build the hash function is surprisingly low: (we only need to do it once): +The construction time required to build the hash function is surprisingly low, and we only need to do it once: | Volume | `ph::Function` (construct) | PHF size | |--------|----------------------------|----------| | 1M | 52ms | 0.34Mb | | 100M | 7.4s | 33.7Mb | -Usage of PHF in Qdrant allows us to minimize latency of cold reads, which is especially important for large-scale multi-tenant systems. -With PHF, it is enough to read a single page from a disk to get the exact location of the data. +The usage of PHF in Qdrant lets us minimize the latency of cold reads, which is especially important for large-scale multi-tenant systems. With PHF, it is enough to read a single page from a disk to get the exact location of the data. ### Defragmentation When you read data from a disk, you almost never read a single byte. Instead, you read a page, which is a fixed-size chunk of data. On many systems, the page size is 4KB, which means that every read operation will read 4KB of data, even if you only need a single byte. -Vector Search, on the other hand, requires reading a lot of small vectors, which might create a large overhead. +Vector search, on the other hand, requires reading a lot of small vectors, which might create a large overhead. It is especially noticeable if we use binary quantization, where the size of even large OpenAI 1536d vectors is compressed down to **192 bytes**. {{< figure src="/articles_data/immutable-data-structures/page-vector.png" alt="Overhead when reading single vector" caption="Overhead when reading single vector" width="80%" >}} @@ -168,16 +166,16 @@ If we knew some additional information about the data, we could combine all rele {{< figure src="/articles_data/immutable-data-structures/defragmentation.png" alt="Defragmentation" caption="Defragmentation" width="70%" >}} -This additional information is available to Qdrant via the payload index. +This additional information is available to Qdrant via the [payload index](/documentation/concepts/indexing/#payload-index). By specifying the payload index, which is going to be used for filtering most of the time, we can put all vectors with the same payload together. This way, reading a single page will also read nearby vectors, which will be used in the search. -This approach is especially efficient for multi-tenant systems, where only a small subset of vectors is actively used for search. +This approach is especially efficient for [multi-tenant systems](/documentation/guides/multiple-partitions/), where only a small subset of vectors is actively used for search. Capacity of such deployment is typically defined by the size of hot subset, which is much smaller than the total number of vectors. -Grouping relevant vectors together allows us to optimize the size of the hot subset by avoiding caching of irrelevant data. -Here are some benchmark data we have for comparing defragmented and non-defragmented storage: +> Grouping relevant vectors together allows us to optimize the size of the hot subset by avoiding caching of irrelevant data. +The following benchmark data compares RPS for defragmented and non-defragmented storage: | % of hot subset | Tenant Size (vectors) | RPS, Non-defragmented | RPS, Defragmented | |-----------------|-----------------------|-----------------------|-------------------| @@ -193,19 +191,19 @@ Here are some benchmark data we have for comparing defragmented and non-defragme | 100% | 5k | 2.7 | 95 | -Dataset size: 2M 768d vectors (~6Gb Raw data), binary quantization, 650Mb of RAM limit. +**Dataset size:** 2M 768d vectors (~6Gb Raw data), binary quantization, 650Mb of RAM limit. All benchmarks are made with minimal RAM allocation to demonstrate disk cache efficiency. As you can see, the biggest impact is on the small tenant size, where defragmentation allows us to achieve **100x more RPS**. Of course, the real-world impact of defragmentation depends on the specific workload and the size of the hot subset, but enabling this feature can significantly improve the performance of Qdrant. -Please find more details on how to enable defragmentation in the [index documentation](/documentation/concepts/indexing/#tenant-index). +Please find more details on how to enable defragmentation in the [indexing documentation](/documentation/concepts/indexing/#tenant-index). ## Updating Immutable Data Structures One may wonder how Qdrant allows updating collection data if everything is immutable. -Indeed, Qdrant API allows the change of any vector or payload at any time, so from the user's perspective, the whole collection is mutable at any time. +Indeed, [Qdrant API](https://api.qdrant.tech) allows the change of any vector or payload at any time, so from the user's perspective, the whole collection is mutable at any time. As it usually happens with every decent magic trick, the secret is disappointingly simple: not all data in Qdrant is immutable. In Qdrant, we storage is divided into segments, which might be either mutable or immutable.

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