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| <p>An implementation of the Log-Structured Merge Tree (LSM tree) data | ||
| structure in Java.</p> | ||
| <p><strong>Table of Contents</strong></p> | ||
| <ol type="1"> | ||
| <li><a href="#Architecture">Architecture</a> | ||
| <ol type="1"> | ||
| <li><a href="#SSTable">SSTable</a></li> | ||
| <li><a href="#Skip-List">Skip-List</a></li> | ||
| <li><a href="#Tree">Tree</a></li> | ||
| </ol></li> | ||
| <li><a href="#Benchmarks">Benchmarks</a> | ||
| <ol type="1"> | ||
| <li><a href="#sstable-1">SSTable</a></li> | ||
| <li><a href="#skip-list-1">Skip-List</a></li> | ||
| <li><a href="#tree-1">Tree</a></li> | ||
| </ol></li> | ||
| <li><a href="#possible-improvements">Possible future | ||
| improvements</a></li> | ||
| <li><a href="#references">References</a></li> | ||
| </ol> | ||
| <p>To interact with a toy tree you can use <code>./gradlew run -q</code> | ||
| to spawn a console.</p> | ||
| <figure> | ||
| <img src="misc%2Fconsole.png" alt="console.png" /> | ||
| <figcaption aria-hidden="true">console.png</figcaption> | ||
| </figure> | ||
| <hr /> | ||
| <h1 data-number="1" id="architecture"><span | ||
| class="header-section-number">1</span> Architecture</h1> | ||
| <p>Architecture overview, from SSTables, which are the disk-resident | ||
| portion of the database, Skip Lists, used as memory buffers, and finally | ||
| to the combination of the twos to create insertion, lookup and deletion | ||
| primitives.</p> | ||
| <h2 data-number="1.1" id="sstable"><span | ||
| class="header-section-number">1.1</span> SSTable</h2> | ||
| <p>Sorted String Table (SSTable) is a collection of files modelling | ||
| key-value pairs in sorted order by key. It is used as a persistent | ||
| storage for the LSM tree.</p> | ||
| <h3 data-number="1.1.1" id="components"><span | ||
| class="header-section-number">1.1.1</span> Components</h3> | ||
| <ul> | ||
| <li><em>Data</em>: key-value pairs in sorted order by key, stored in a | ||
| file;</li> | ||
| <li><em>Sparse index</em>: sparse index containing key and offset of the | ||
| corresponding key-value pair in the data;</li> | ||
| <li><em>Bloom filter</em>: a <a | ||
| href="https://en.wikipedia.org/wiki/Bloom_filter">probabilistic data | ||
| structure</a> used to test whether a key is in the SSTable.</li> | ||
| </ul> | ||
| <h3 data-number="1.1.2" id="key-lookup"><span | ||
| class="header-section-number">1.1.2</span> Key lookup</h3> | ||
| <p>The basic idea is to use the sparse index to find the key-value pair | ||
| in the data file. The steps are:</p> | ||
| <ol type="1"> | ||
| <li>Use the Bloom filter to test whether the key might be in the | ||
| table;</li> | ||
| <li>If the key might be present, use binary search on the index to find | ||
| the maximum lower bound of the key;</li> | ||
| <li>Scan the data from the position found in the previous step to find | ||
| the key-value pair. The search can stop when we are seeing a key greater | ||
| than the one we are looking for, or when we reach the end of the | ||
| table.</li> | ||
| </ol> | ||
| <p>The search is as lazy as possible, meaning that we read the minimum | ||
| amount of data from disk, for instance, if the next key length is | ||
| smaller than the one we are looking for, we can skip the whole key-value | ||
| pair.</p> | ||
| <h3 data-number="1.1.3" id="persistence"><span | ||
| class="header-section-number">1.1.3</span> Persistence</h3> | ||
| <p>A table is persisted to disk when it is created. A base filename is | ||
| defined, and three files are present:</p> | ||
| <ul> | ||
| <li><code><base_filename>.data</code>: data file;</li> | ||
| <li><code><base_filename>.index</code>: index file;</li> | ||
| <li><code><base_filename>.bloom</code>: bloom filter file.</li> | ||
| </ul> | ||
| <p><strong>Data format</strong></p> | ||
| <ul> | ||
| <li><code>n</code>: number of key-value pairs;</li> | ||
| <li><code><key_len_1, value_len_1, key_1, value_1, ... key_n, value_n></code>: | ||
| key-value pairs.</li> | ||
| </ul> | ||
| <p><strong>Index format</strong></p> | ||
| <ul> | ||
| <li><code>s</code>: number of entries in the whole table;</li> | ||
| <li><code>n</code>: number of entries in the index;</li> | ||
| <li><code>o_1, o_2 - o_1, ..., o_n - o_n-1</code>: offsets of the | ||
| key-value pairs in the data file, skipping the first one;</li> | ||
| <li><code>s_1, s_2, ..., s_n</code>: remaining keys after a sparse index | ||
| entry, used to exit from search;</li> | ||
| <li><code><key_len_1, key_1, ... key_len_n, key_n></code>: keys in | ||
| the index.</li> | ||
| </ul> | ||
| <p><strong>Filter format</strong></p> | ||
| <ul> | ||
| <li><code>m</code>: number of bits in the bloom filter;</li> | ||
| <li><code>k</code>: number of hash functions;</li> | ||
| <li><code>n</code>: size of underlying long array;</li> | ||
| <li><code>b_1, b_2, ..., b_n</code>: bits of the bloom filter.</li> | ||
| </ul> | ||
| <p>To save space, all integers are stored in <a | ||
| href="https://nlp.stanford.edu/IR-book/html/htmledition/variable-byte-codes-1.html">variable-length | ||
| encoding</a>, and offsets in the index are stored as <a | ||
| href="https://en.wikipedia.org/wiki/Delta_encoding">deltas</a>.</p> | ||
| <hr /> | ||
| <h2 data-number="1.2" id="skip-list"><span | ||
| class="header-section-number">1.2</span> Skip-List</h2> | ||
| <p>A <a href="https://en.wikipedia.org/wiki/Skip_list">skip-list</a> is | ||
| a probabilistic data structure that allows fast search, insertion and | ||
| deletion of elements in a sorted sequence.</p> | ||
| <p>In the LSM tree, it is used as an in-memory data structure to store | ||
| key-value pairs in sorted order by key. Once the skip-list reaches a | ||
| certain size, it is flushed to disk as an SSTable.</p> | ||
| <h3 data-number="1.2.1" id="operations-details"><span | ||
| class="header-section-number">1.2.1</span> Operations details</h3> | ||
| <p>The idea of a skip list is similar to a classic linked list. We have | ||
| nodes with forward pointers, but also levels. We can think about a level | ||
| as a fast lane between nodes. By carefully constructing them at | ||
| insertion time, searches are faster, as they can use higher levels to | ||
| skip unwanted nodes.</p> | ||
| <p>Given <code>n</code> elements, a skip list has <code>log(n)</code> | ||
| levels, the first level containing all the elements. By increasing the | ||
| level, the number of elements is cut roughly by half.</p> | ||
| <p>To locate an element, we start from the top level and move forward | ||
| until we find an element greater than the one we are looking for. Then | ||
| we move down to the next level and repeat the process until we find the | ||
| element.</p> | ||
| <p>Insertions, deletions, and updates are done by first locating the | ||
| element, then performing the operation on the node. All of them have an | ||
| average time complexity of <code>O(log(n))</code>.</p> | ||
| <hr /> | ||
| <h2 data-number="1.3" id="tree"><span | ||
| class="header-section-number">1.3</span> Tree</h2> | ||
| <p>Having defined SSTables and Skip Lists we can obtain the final | ||
| structure as a combination of the two. The main idea is to use the | ||
| latter as an in-memory buffer, while the former efficiently stores | ||
| flushed buffers.</p> | ||
| <h3 data-number="1.3.1" id="insertion"><span | ||
| class="header-section-number">1.3.1</span> Insertion</h3> | ||
| <p>Each insert goes directly to a Memtable, which is a Skip List under | ||
| the hood, so the response time is quite fast. There exists a threshold, | ||
| over which the mutable structure is made immutable by appending it to | ||
| the <em>immmutable memtables LIFO list</em> and replaced with a new | ||
| mutable list.</p> | ||
| <p>The immutable memtable list is asynchronously consumed by a | ||
| background thread, which takes the next available list and create a | ||
| disk-resident SSTable with its content.</p> | ||
| <h3 data-number="1.3.2" id="lookup"><span | ||
| class="header-section-number">1.3.2</span> Lookup</h3> | ||
| <p>While looking for a key, we proceed as follows:</p> | ||
| <ol type="1"> | ||
| <li>Look into the in-memory buffer, if the key is recently written it is | ||
| likely here, if not present continue;</li> | ||
| <li>Look into the immutable memtables list, iterating from the most | ||
| recent to the oldest, if not present continue;</li> | ||
| <li>Look into disk tables, iterating from the most recent one to the | ||
| oldest, if not present return null.</li> | ||
| </ol> | ||
| <h3 data-number="1.3.3" id="deletions"><span | ||
| class="header-section-number">1.3.3</span> Deletions</h3> | ||
| <p>To delete a key, we do not need to delete all its replicas, from the | ||
| on-disk tables, we just need a special value called <em>tombstone</em>. | ||
| Hence a deletion is the same as an insertion, but with a value set to | ||
| null. While looking for a key, if we encounter a null value we simply | ||
| return null as a result.</p> | ||
| <h3 data-number="1.3.4" id="sstable-compaction"><span | ||
| class="header-section-number">1.3.4</span> SSTable Compaction</h3> | ||
| <p>The most expensive operation while looking for a key is certainly the | ||
| disk search, and this is why bloom filters are crucial for negative | ||
| lookup on SSTables. But no bloom filter can save us if too many tables | ||
| are available to search, hence we need <em>compaction</em>.</p> | ||
| <p>When flushing a Memtable, we create an SSTable of level one. When the | ||
| first level reaches a certain threshold, all its tables are merged into | ||
| a level-two table, and so on. This permits us to save storage and query | ||
| fewer tables in lookups.</p> | ||
| <p>Note that this style of compaction is not standard, there are various | ||
| sophisticated techniques, but for the sake of this project this simple | ||
| level-like compaction works wonders.</p> | ||
| <hr /> | ||
| <h1 data-number="2" id="benchmarks"><span | ||
| class="header-section-number">2</span> Benchmarks</h1> | ||
| <p>I am using <a | ||
| href="https://openjdk.java.net/projects/code-tools/jmh/">JMH</a> to run | ||
| benchmarks, the results are obtained on AMD Ryzen™ 5 4600H with 16GB of | ||
| RAM and 512GB SSD.</p> | ||
| <p>To run them use <code>./gradlew jmh</code>.</p> | ||
| <h2 data-number="2.1" id="sstable-1"><span | ||
| class="header-section-number">2.1</span> SSTable</h2> | ||
| <ul> | ||
| <li>Negative access: the key is not present in the table, hence the | ||
| Bloom filter will likely stop the search;</li> | ||
| <li>Random access: the key is present in the table, the order of the | ||
| keys is random.</li> | ||
| </ul> | ||
| <pre><code> | ||
| Benchmark Mode Cnt Score Error Units | ||
| c.t.l.sstable.SSTableBenchmark.negativeAccess thrpt 5 3316202.976 ± 32851.546 ops/s | ||
| c.t.l.sstable.SSTableBenchmark.randomAccess thrpt 5 7989.945 ± 40.689 ops/s | ||
| </code></pre> | ||
| <h2 data-number="2.2" id="bloom-filter"><span | ||
| class="header-section-number">2.2</span> Bloom filter</h2> | ||
| <ul> | ||
| <li>Add: add keys to a 1M keys Bloom filter with 0.01 false positive | ||
| rate;</li> | ||
| <li>Contains: test whether the keys are present in the Bloom | ||
| filter.</li> | ||
| </ul> | ||
| <pre><code>Benchmark Mode Cnt Score Error Units | ||
| c.t.l.bloom.BloomFilterBenchmark.add thrpt 5 3190753.307 ± 74744.764 ops/s | ||
| c.t.l.bloom.BloomFilterBenchmark.contains thrpt 5 3567392.634 ± 220377.613 ops/s | ||
| </code></pre> | ||
| <h2 data-number="2.3" id="skip-list-1"><span | ||
| class="header-section-number">2.3</span> Skip-List</h2> | ||
| <ul> | ||
| <li>Get: get keys from a 100k keys skip-list;</li> | ||
| <li>Add/Remove: add and remove keys from a 100k keys skip-list.</li> | ||
| </ul> | ||
| <pre><code> | ||
| Benchmark Mode Cnt Score Error Units | ||
| c.t.l.memtable.SkipListBenchmark.addRemove thrpt 5 430239.471 ± 4825.990 ops/s | ||
| c.t.l.memtable.SkipListBenchmark.get thrpt 5 487265.620 ± 8201.227 ops/s | ||
| </code></pre> | ||
| <h2 data-number="2.4" id="tree-1"><span | ||
| class="header-section-number">2.4</span> Tree</h2> | ||
| <ul> | ||
| <li>Get: get elements from a tree with 1M keys;</li> | ||
| <li>Add: add 1M distinct elements to a tree with a memtable size of | ||
| 2^18</li> | ||
| </ul> | ||
| <pre><code>Benchmark Mode Cnt Score Error Units | ||
| c.t.l.tree.LSMTreeAddBenchmark.add thrpt 5 540788.751 ± 54491.134 ops/s | ||
| c.t.l.tree.LSMTreeGetBenchmark.get thrpt 5 9426.951 ± 241.190 ops/s | ||
| </code></pre> | ||
| <hr /> | ||
| <h2 data-number="2.5" id="possible-improvements"><span | ||
| class="header-section-number">2.5</span> Possible improvements</h2> | ||
| <p>There is certainly space for improvement on this project:</p> | ||
| <ol type="1"> | ||
| <li>Blocked bloom filters: its a variant of a classic array-like bloom | ||
| filter which is more cache efficient;</li> | ||
| <li>Search fingers in the Skip list: the idea is to keep a pointer to | ||
| the last search, and start from there with subsequent queries;</li> | ||
| <li>Proper level compaction in the LSM tree;</li> | ||
| <li>Write ahead log for the insertions, without this, a crash makes all | ||
| the in-memory writes disappear;</li> | ||
| <li>Proper recovery: handle crashes and reboots, using existing SSTables | ||
| and the write-ahead log.</li> | ||
| </ol> | ||
| <p>I don’t have the practical time to do all of this, perhaps the first | ||
| two points will be handled in the future.</p> | ||
| <hr /> | ||
| <h2 data-number="2.6" id="references"><span | ||
| class="header-section-number">2.6</span> References</h2> | ||
| <ul> | ||
| <li><a href="https://www.databass.dev/">Database Internals</a> by Alex | ||
| Petrov, specifically chapters about Log-Structured Storage and File | ||
| Formats;</li> | ||
| <li><a | ||
| href="https://api.drum.lib.umd.edu/server/api/core/bitstreams/17176ef8-8330-4a6c-8b75-4cd18c570bec/content">A | ||
| Skip List Cookbook</a> by William Pugh.</li> | ||
| </ul> | ||
| <hr /> | ||
| <p><em>If you found this useful or interesting do not hesitate to ask | ||
| clarifying questions or get in touch!</em></p> |
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