Manifest in openkv itself is a tiny db with WAL of operations to the system and a snapshot.
Snapshot:
-version
+version: String
data_file_bitmaps: {
"4mb": Bitmap
@@ -147,21 +147,30 @@ Manifest
}
spans: [
-{
- start: String
- end: String
- vsst: {
- 0: [VS1, VS2, ...]
- 1: [VSi, VSj, ...],
+ {
+ start: String
+ end: String
+ vsstables: {
+ 0: [VSST1, VSST2, ...]
+ 1: [VSSTi, VSSTj, ...],
+ }
+ },
+ ...
+]
- }
+separated_values: [
+ {
+ start_value_id: String,
+ end_value_id: String
+ vsstables: {
+ 0: [VSST1, VSST2, ...]
+ 1: [VSSTi, VSSTj, ...],
+ }
-}
+ },
+ ...
]
-
-
-
diff --git a/print.html b/print.html
index 188e168..4cee217 100644
--- a/print.html
+++ b/print.html
@@ -422,7 +422,7 @@ Commit a SS
Manifest
Manifest in openkv itself is a tiny db with WAL of operations to the system and a snapshot.
Snapshot:
-version
+version: String
data_file_bitmaps: {
"4mb": Bitmap
@@ -430,21 +430,30 @@ Manifest
}
spans: [
-{
- start: String
- end: String
- vsst: {
- 0: [VS1, VS2, ...]
- 1: [VSi, VSj, ...],
+ {
+ start: String
+ end: String
+ vsstables: {
+ 0: [VSST1, VSST2, ...]
+ 1: [VSSTi, VSSTj, ...],
+ }
+ },
+ ...
+]
- }
+separated_values: [
+ {
+ start_value_id: String,
+ end_value_id: String
+ vsstables: {
+ 0: [VSST1, VSST2, ...]
+ 1: [VSSTi, VSSTj, ...],
+ }
-}
+ },
+ ...
]
-
-
-
diff --git a/searchindex.js b/searchindex.js
index 111d610..7d29199 100644
--- a/searchindex.js
+++ b/searchindex.js
@@ -1 +1 @@
-Object.assign(window.search, {"doc_urls":["arch/memtable.html#memtable","arch/memtable.html#flush","arch/sstable.html#sstable","arch/sstable.html#header","arch/sstable.html#metas","arch/sstable.html#index","arch/sstable.html#caching","arch/sstable.html#sparse-index","arch/sstable.html#records","arch/sstable.html#checksum","arch/sstable.html#positive-and-negative-sstable","arch/sstable.html#reading-a-record","arch/sstable.html#performance-considerations","arch/virtual-sstable.html#virtual-sstable","arch/separate-value.html#separate-value","arch/sharding.html#sharding","arch/sharding.html#sub-lsm","arch/sharding.html#split-and-merge","arch/compaction.html#compaction","arch/min-hash.html#min-hash","arch/min-hash.html#jaccard-similarity","arch/min-hash.html#estimate-the-number-of-common-keys","arch/min-hash.html#estimate-the-probability","arch/min-hash.html#generate-signature-for-a-sstable","arch/min-hash.html#calculate-similarity-of-two-sstable","arch/min-hash.html#simulation","arch/min-hash.html#optimize-compaction-with-min-hash","arch/datafile.html#datafile","arch/datafile.html#commit-a-sstable","arch/manifest.html#manifest"],"index":{"documentStore":{"docInfo":{"0":{"body":18,"breadcrumbs":2,"title":1},"1":{"body":25,"breadcrumbs":2,"title":1},"10":{"body":73,"breadcrumbs":4,"title":3},"11":{"body":21,"breadcrumbs":3,"title":2},"12":{"body":51,"breadcrumbs":3,"title":2},"13":{"body":30,"breadcrumbs":4,"title":2},"14":{"body":10,"breadcrumbs":4,"title":2},"15":{"body":75,"breadcrumbs":3,"title":1},"16":{"body":8,"breadcrumbs":4,"title":2},"17":{"body":18,"breadcrumbs":4,"title":2},"18":{"body":24,"breadcrumbs":2,"title":1},"19":{"body":15,"breadcrumbs":5,"title":2},"2":{"body":20,"breadcrumbs":2,"title":1},"20":{"body":59,"breadcrumbs":5,"title":2},"21":{"body":8,"breadcrumbs":7,"title":4},"22":{"body":15,"breadcrumbs":5,"title":2},"23":{"body":31,"breadcrumbs":6,"title":3},"24":{"body":14,"breadcrumbs":7,"title":4},"25":{"body":151,"breadcrumbs":4,"title":1},"26":{"body":44,"breadcrumbs":7,"title":4},"27":{"body":45,"breadcrumbs":3,"title":1},"28":{"body":21,"breadcrumbs":4,"title":2},"29":{"body":28,"breadcrumbs":2,"title":1},"3":{"body":8,"breadcrumbs":2,"title":1},"4":{"body":39,"breadcrumbs":2,"title":1},"5":{"body":46,"breadcrumbs":2,"title":1},"6":{"body":7,"breadcrumbs":2,"title":1},"7":{"body":41,"breadcrumbs":3,"title":2},"8":{"body":28,"breadcrumbs":2,"title":1},"9":{"body":4,"breadcrumbs":2,"title":1}},"docs":{"0":{"body":"MemTable in LSM is the in-memory representation of key-value pairs. It can be considered as a BTreeMap. There is only one active MemTable for every openkv instance. Memtable is shared by all sub-LSM","breadcrumbs":"MemTable » MemTable","id":"0","title":"MemTable"},"1":{"body":"Flush MemTable to SSTable. If the MemTable becomes too large, flush one continous portion(span) into a sub-LSM. MemTable always flushes the biggest span, e.g., the one with most keys, unless there is a pressure to reclaim WAL space.","breadcrumbs":"MemTable » Flush","id":"1","title":"Flush"},"10":{"body":"One flush builds 2 SSTable: One of them contains all inserted or updated records, the Positive SSTable. The other one contains only deleted records, i.e., tomobstones: the Negative SSTable. Both has the same level and the same key range . In other word, we store updated recoreds and deleted records separately. Records part in P-SSTable:Records part in N-SSTable:key-suffixkey-suffix...key-suffixkey-suffix...seqseq...seqseq...valuevalue... By separating P/N records, it is possible to compact a N-SSTable down to reclaim space quickly. E.g., a Negative SSTable N1 can be pushed down and be merged with N2 and N3, without touching P1. Because to N1, P1 is transparent : N1 ∩ P1 = ø N2P2N1P1N3P3","breadcrumbs":"SSTable » Positive and Negative SSTable","id":"10","title":"Positive and Negative SSTable"},"11":{"body":"Search the key in the Index. If it matches a path in the trie, scan Records from the offset upto next offset to find the record. If the key-suffix also matches the search key, returns the value.","breadcrumbs":"SSTable » Reading a record","id":"11","title":"Reading a record"},"12":{"body":"Trie naturally compresses prefixes and an SSTable only stores a small range of keys thus the space cost is low enough. For a static trie, succinct data structure can be adopted to reduce the size of the trie. Our goal budget for a key is about several bytes. So that keeping the Index in memory is possible and unnecessary IO can be reduced. Trie is not cache friendly thus a single trie should not be very large. The expected time cost for a query in the Index is less than 200 ns.","breadcrumbs":"SSTable » Performance considerations","id":"12","title":"Performance considerations"},"13":{"body":"VSSTable is a unit to manage SSTable. Because an SSTable may be referenced more than once: e.g. when splitting a span. V1T1V4T4V2T2V5T5V3T3splitV1T1V4T4V2T2V2'V5T5V3T3 A SSTable is removed when there is no VSSTable referencing it. A VSSTable has a key range that is subset of the SSTable it references. struct VSSTable { key_start: String, key_end: String, sstable: SSTableId,\n}","breadcrumbs":"Virtual SSTable » Virtual SSTable","id":"13","title":"Virtual SSTable"},"14":{"body":"flush to SSTable with separate valuek3 is removed at level-0 by compaction:k1bark1bark2vid2k2vid2k3vid3k3vid3Separate values:Separate values:vid2v2vid3vid2v2vid3v3...vid3v3............vidivividiviTombstonevidjvjvidjvj............","breadcrumbs":"Separate Value » Separate value","id":"14","title":"Separate value"},"15":{"body":"One of the performance issue about LSM tree is the write/read amplification. When a db becomes bigger, the number of levels(l) in a LSM becomes increases, in logarithm order. A record will be rewritten( compaction ) l times to enter the bottom level. Assumes the fanout of every level is n, every record amplifies write IO by O(l) * n times. By splitting LSM into several smaller ones, l becomes smaller and the write/read amplification will be reduced. Thus openkv organize its data in a way resembles to a two-level BTree: The btree root node is a array of all sub-LSM, sorted in key order. Each of the leaf nodes is a small LSM. L0L1L3L2L0L1L0L0(-oo, b]L2L1L0[b, e)L0[e, +oo)L2L1L0","breadcrumbs":"Internal Sharding » Sharding","id":"15","title":"Sharding"},"16":{"body":"Sub-LSM is a small LSM tree, with a limited number of levels.","breadcrumbs":"Internal Sharding » Sub-LSM","id":"16","title":"Sub-LSM"},"17":{"body":"A sub-LSM will be split if the level exceeds a threshold(e.g., 3). Two adjacent sub-LSM is merged into one if both of them becomes lower than 1/3 of the threshold.","breadcrumbs":"Internal Sharding » Split and Merge","id":"17","title":"Split and Merge"},"18":{"body":"Push a SSTable down and merge it with all overlapping SSTable at the next lower level. Leave only the record with the greatest seq when merging. When reaching the bottom level, i.e, level-0, a tombstone record can be removed for good.","breadcrumbs":"Compaction » Compaction","id":"18","title":"Compaction"},"19":{"body":"min-hash is a signature of all keys in a SSTable and is used to optimize the compaction. E.g., find out a pair of SSTable with most common keys.","breadcrumbs":"Compaction » min-hash » Min-hash","id":"19","title":"Min-hash"},"2":{"body":"A SSTable(solid-state table) is the same concept used in levelDB or rocksDB. The size of an SSTable can only be 4MB(for tombstone only SSTable) or 16MB(regular SSTable). The data layout inside an SSTable: HeaderMetasIndexRecordsChecksum","breadcrumbs":"SSTable » SSTable","id":"2","title":"SSTable"},"20":{"body":"Let U be a set and A and B be subsets of U, then the Jaccard index is defined to be the ratio of the number of elements of their intersection and the number of elements of their union: J(A,B)=∣A∪B∣∣A∩B∣. Let h be a hash function that maps the members of U to distinct integers, e.g., let h(x) = SHA1(x). For any set S, define H_min(S) to be the minimal integer(hash value) of members in S: H_min(S) = min({h(x) | x ∈ S}) Now, applying H_min to both A and B, and assuming no hash collisions, the probability that H_min(A) == H_min(B) is true is equal to the similarity J(A,B): Pr[ H_min(A) = H_min(B) ] = J(A,B)","breadcrumbs":"Compaction » min-hash » Jaccard similarity","id":"20","title":"Jaccard similarity"},"21":{"body":"Given two SSTable, the number of common keys can be calculated with: c=1+pp(∣A∣+∣B∣)","breadcrumbs":"Compaction » min-hash » Estimate the number of common keys","id":"21","title":"Estimate the number of common keys"},"22":{"body":"The probability can be estimiated with y/k, where k is the number of different hash functions and y is the number of hash functions hᵢ for which hᵢ(A) == hᵢ(B)","breadcrumbs":"Compaction » min-hash » Estimate the Probability","id":"22","title":"Estimate the Probability"},"23":{"body":"fn gen_sstable_signature(sstable: &SSTable, number_of_hashes: usize) -> Vec{ // Result signature let signature = Vec::with_capacity(number_of_hashes); // Distribute hash values to `k` buckets to simulate `k` hash functions. let buckets = Vec::with_capacity(number_of_hashes); for k in sstable.keys() { let h = SHA1(k) as u64; buckets[h%number_of_hashes].push(h); } for i in 0..number_of_hashes { signature[i] = min(buckets[i]); } signature\n}","breadcrumbs":"Compaction » min-hash » Generate signature for a SSTable","id":"23","title":"Generate signature for a SSTable"},"24":{"body":"fn calc_sig(a: &SSTable, b:&SSTable) -> f64 { let eq = 0.0; for i in 0..number_of_hashes: if a.signature[i] == a.signature[i] { eq += 1 } eq / number_of_hashes }","breadcrumbs":"Compaction » min-hash » Calculate similarity of two SSTable","id":"24","title":"Calculate similarity of two SSTable"},"25":{"body":"We provides a python script min-hash.py to estimate the accuracy of this algo. Config value Number of hash functions(buckets) 128 Hash value u64 Space cost sizeof(u64) * 128 = 1KB Actual vs Estimated: |A∪B| |A| |B| Actual (A∩B)/(A∪B)% Estimated% error% 1000 360 840 20.00% 21.88% 1.87% 1000 520 880 40.00% 38.28% -1.72% 1000 680 920 60.00% 60.94% 0.94% 1000 839 959 80.16% 78.91% -1.25% 1000 1000 1000 100.00% 100.00% 0.00% 10000 3600 8400 20.00% 15.62% -4.38% 10000 5200 8800 40.00% 35.16% -4.84% 10000 6800 9200 60.00% 60.94% 0.94% 10000 8399 9599 80.02% 85.16% 5.14% 10000 10000 10000 100.00% 100.00% 0.00% 100000 36000 84000 20.00% 21.88% 1.87% 100000 52000 88000 40.00% 47.66% 7.66% 100000 68000 92000 60.00% 62.50% 2.50% 100000 83999 95999 80.00% 80.47% 0.47% 100000 100000 100000 100.00% 100.00% 0.00% 1000000 360000 840000 20.00% 19.53% -0.47% 1000000 520000 880000 40.00% 40.62% 0.62% 1000000 680000 920000 60.00% 58.59% -1.41% 1000000 839999 959999 80.00% 75.78% -4.22% 1000000 1000000 1000000 100.00% 100.00% 0.00%","breadcrumbs":"Compaction » min-hash » Simulation","id":"25","title":"Simulation"},"26":{"body":"With min-hash we can find the best choice to compact. For every SSTable, calculate the Jaccard index of it and the overlapping SSTable at the lower level. Push down the one with the max Jaccard index. The space cost is negligible. Only 1KB more space for every SSTable. The time complexity is O(n), where n is the number of SSTable in the system. Because for every SSTable, there are about only k SSTable that have overlapping key range with it.where k is the level fanout.","breadcrumbs":"Compaction » min-hash » Optimize compaction with min-hash","id":"26","title":"Optimize compaction with min-hash"},"27":{"body":"Multiple SSTable are stored in a large file, the DataFile. DataFile only allocates or reclaims space by a fixed size: its allocation unit. There is one DataFile for each allocation unit. Assuming in openkv the allocation unit are 4MB and 16MB, then there are two DataFiles: df-4mb and df-16mb. Each DataFile has a corresponding bitmap for tracking allocated unit. The bitmap is part of the manifest bitmap-4mb:DataFile-4mb:bitmap-16mb:1SST01...00111100SST0SST0...","breadcrumbs":"Data File » DataFile","id":"27","title":"DataFile"},"28":{"body":"Find the first 0 in df-bitmap. This bitmap has to be indexed to speed up searching for the first 0. Flush and fsync SSTable data to DataFile. Flush and fsync bitmap in manifest .","breadcrumbs":"Data File » Commit a SSTable","id":"28","title":"Commit a SSTable"},"29":{"body":"Manifest in openkv itself is a tiny db with WAL of operations to the system and a snapshot. Snapshot: version data_file_bitmaps: { \"4mb\": Bitmap \"16mb\": Bitmap\n} spans: [\n{ start: String end: String vsst: { 0: [VS1, VS2, ...] 1: [VSi, VSj, ...], } } ]","breadcrumbs":"Manifest » Manifest","id":"29","title":"Manifest"},"3":{"body":"Header is fix-sized and contains an SSTable format version etc.","breadcrumbs":"SSTable » Header","id":"3","title":"Header"},"4":{"body":"Metas stores configs of this SSTable, such as key types, value types, etc. E.g., a fix-sized key or value may use a type-specific store format. Fix-sized key does not need to store key-suffix in Records segment. TODO: prove it. Metas also stores the cardinality signature of all keys to optimize SSTable compaction.","breadcrumbs":"SSTable » Metas","id":"4","title":"Metas"},"5":{"body":"Index is a trie built from all keys stored in this SSTable, without single-branch tail. The leaf node in the trie stored the corresponding offset of a record in Records. It contains enough info to locate a present key in the Records segment. But there could be a false-positive for a key not in Records. For a given example of 3 key values: fantastice: 1\nfoo: 5\nfood: 3 The Index would be like this: faooffset for fantasticeooffset of foodoffset of food","breadcrumbs":"SSTable » Index","id":"5","title":"Index"},"6":{"body":"Index is preferred to reside in memory, while the Records is left on disk.","breadcrumbs":"SSTable » Caching","id":"6","title":"Caching"},"7":{"body":"Not all keys in the Index has a corresponding offset stored for it. Since the IO optimization should be IO-oriented, reading several bytes may cost almost the same resource as reading several kilo-bytes. Thus the Index only need to store an offset for several adjacent keys. And we just need to limit the distance between two adjacent offsets in the Index to be less than a expected value, e.g., 16 KB.","breadcrumbs":"SSTable » Sparse Index","id":"7","title":"Sparse Index"},"8":{"body":"The Records segment stores key suffixes that are not included in Index and value. 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It can be considered as a BTreeMap. There is only one active MemTable for every openkv instance. Memtable is shared by all sub-LSM","breadcrumbs":"MemTable » MemTable","id":"0","title":"MemTable"},"1":{"body":"Flush MemTable to SSTable. If the MemTable becomes too large, flush one continous portion(span) into a sub-LSM. MemTable always flushes the biggest span, e.g., the one with most keys, unless there is a pressure to reclaim WAL space.","breadcrumbs":"MemTable » Flush","id":"1","title":"Flush"},"10":{"body":"One flush builds 2 SSTable: One of them contains all inserted or updated records, the Positive SSTable. The other one contains only deleted records, i.e., tomobstones: the Negative SSTable. Both has the same level and the same key range . In other word, we store updated recoreds and deleted records separately. Records part in P-SSTable:Records part in N-SSTable:key-suffixkey-suffix...key-suffixkey-suffix...seqseq...seqseq...valuevalue... By separating P/N records, it is possible to compact a N-SSTable down to reclaim space quickly. E.g., a Negative SSTable N1 can be pushed down and be merged with N2 and N3, without touching P1. Because to N1, P1 is transparent : N1 ∩ P1 = ø N2P2N1P1N3P3","breadcrumbs":"SSTable » Positive and Negative SSTable","id":"10","title":"Positive and Negative SSTable"},"11":{"body":"Search the key in the Index. If it matches a path in the trie, scan Records from the offset upto next offset to find the record. If the key-suffix also matches the search key, returns the value.","breadcrumbs":"SSTable » Reading a record","id":"11","title":"Reading a record"},"12":{"body":"Trie naturally compresses prefixes and an SSTable only stores a small range of keys thus the space cost is low enough. For a static trie, succinct data structure can be adopted to reduce the size of the trie. Our goal budget for a key is about several bytes. So that keeping the Index in memory is possible and unnecessary IO can be reduced. Trie is not cache friendly thus a single trie should not be very large. The expected time cost for a query in the Index is less than 200 ns.","breadcrumbs":"SSTable » Performance considerations","id":"12","title":"Performance considerations"},"13":{"body":"VSSTable is a unit to manage SSTable. Because an SSTable may be referenced more than once: e.g. when splitting a span. V1T1V4T4V2T2V5T5V3T3splitV1T1V4T4V2T2V2'V5T5V3T3 A SSTable is removed when there is no VSSTable referencing it. A VSSTable has a key range that is subset of the SSTable it references. struct VSSTable { key_start: String, key_end: String, sstable: SSTableId,\n}","breadcrumbs":"Virtual SSTable » Virtual SSTable","id":"13","title":"Virtual SSTable"},"14":{"body":"flush to SSTable with separate valuek3 is removed at level-0 by compaction:k1bark1bark2vid2k2vid2k3vid3k3vid3Separate values:Separate values:vid2v2vid3vid2v2vid3v3...vid3v3............vidivividiviTombstonevidjvjvidjvj............","breadcrumbs":"Separate Value » Separate value","id":"14","title":"Separate value"},"15":{"body":"One of the performance issue about LSM tree is the write/read amplification. When a db becomes bigger, the number of levels(l) in a LSM becomes increases, in logarithm order. A record will be rewritten( compaction ) l times to enter the bottom level. Assumes the fanout of every level is n, every record amplifies write IO by O(l) * n times. By splitting LSM into several smaller ones, l becomes smaller and the write/read amplification will be reduced. Thus openkv organize its data in a way resembles to a two-level BTree: The btree root node is a array of all sub-LSM, sorted in key order. Each of the leaf nodes is a small LSM. L0L1L3L2L0L1L0L0(-oo, b]L2L1L0[b, e)L0[e, +oo)L2L1L0","breadcrumbs":"Internal Sharding » Sharding","id":"15","title":"Sharding"},"16":{"body":"Sub-LSM is a small LSM tree, with a limited number of levels.","breadcrumbs":"Internal Sharding » Sub-LSM","id":"16","title":"Sub-LSM"},"17":{"body":"A sub-LSM will be split if the level exceeds a threshold(e.g., 3). Two adjacent sub-LSM is merged into one if both of them becomes lower than 1/3 of the threshold.","breadcrumbs":"Internal Sharding » Split and Merge","id":"17","title":"Split and Merge"},"18":{"body":"Push a SSTable down and merge it with all overlapping SSTable at the next lower level. Leave only the record with the greatest seq when merging. When reaching the bottom level, i.e, level-0, a tombstone record can be removed for good.","breadcrumbs":"Compaction » Compaction","id":"18","title":"Compaction"},"19":{"body":"min-hash is a signature of all keys in a SSTable and is used to optimize the compaction. E.g., find out a pair of SSTable with most common keys.","breadcrumbs":"Compaction » min-hash » Min-hash","id":"19","title":"Min-hash"},"2":{"body":"A SSTable(solid-state table) is the same concept used in levelDB or rocksDB. The size of an SSTable can only be 4MB(for tombstone only SSTable) or 16MB(regular SSTable). The data layout inside an SSTable: HeaderMetasIndexRecordsChecksum","breadcrumbs":"SSTable » SSTable","id":"2","title":"SSTable"},"20":{"body":"Let U be a set and A and B be subsets of U, then the Jaccard index is defined to be the ratio of the number of elements of their intersection and the number of elements of their union: J(A,B)=∣A∪B∣∣A∩B∣. Let h be a hash function that maps the members of U to distinct integers, e.g., let h(x) = SHA1(x). For any set S, define H_min(S) to be the minimal integer(hash value) of members in S: H_min(S) = min({h(x) | x ∈ S}) Now, applying H_min to both A and B, and assuming no hash collisions, the probability that H_min(A) == H_min(B) is true is equal to the similarity J(A,B): Pr[ H_min(A) = H_min(B) ] = J(A,B)","breadcrumbs":"Compaction » min-hash » Jaccard similarity","id":"20","title":"Jaccard similarity"},"21":{"body":"Given two SSTable, the number of common keys can be calculated with: c=1+pp(∣A∣+∣B∣)","breadcrumbs":"Compaction » min-hash » Estimate the number of common keys","id":"21","title":"Estimate the number of common keys"},"22":{"body":"The probability can be estimiated with y/k, where k is the number of different hash functions and y is the number of hash functions hᵢ for which hᵢ(A) == hᵢ(B)","breadcrumbs":"Compaction » min-hash » Estimate the Probability","id":"22","title":"Estimate the Probability"},"23":{"body":"fn gen_sstable_signature(sstable: &SSTable, number_of_hashes: usize) -> Vec{ // Result signature let signature = Vec::with_capacity(number_of_hashes); // Distribute hash values to `k` buckets to simulate `k` hash functions. let buckets = Vec::with_capacity(number_of_hashes); for k in sstable.keys() { let h = SHA1(k) as u64; buckets[h%number_of_hashes].push(h); } for i in 0..number_of_hashes { signature[i] = min(buckets[i]); } signature\n}","breadcrumbs":"Compaction » min-hash » Generate signature for a SSTable","id":"23","title":"Generate signature for a SSTable"},"24":{"body":"fn calc_sig(a: &SSTable, b:&SSTable) -> f64 { let eq = 0.0; for i in 0..number_of_hashes: if a.signature[i] == a.signature[i] { eq += 1 } eq / number_of_hashes }","breadcrumbs":"Compaction » min-hash » Calculate similarity of two SSTable","id":"24","title":"Calculate similarity of two SSTable"},"25":{"body":"We provides a python script min-hash.py to estimate the accuracy of this algo. Config value Number of hash functions(buckets) 128 Hash value u64 Space cost sizeof(u64) * 128 = 1KB Actual vs Estimated: |A∪B| |A| |B| Actual (A∩B)/(A∪B)% Estimated% error% 1000 360 840 20.00% 21.88% 1.87% 1000 520 880 40.00% 38.28% -1.72% 1000 680 920 60.00% 60.94% 0.94% 1000 839 959 80.16% 78.91% -1.25% 1000 1000 1000 100.00% 100.00% 0.00% 10000 3600 8400 20.00% 15.62% -4.38% 10000 5200 8800 40.00% 35.16% -4.84% 10000 6800 9200 60.00% 60.94% 0.94% 10000 8399 9599 80.02% 85.16% 5.14% 10000 10000 10000 100.00% 100.00% 0.00% 100000 36000 84000 20.00% 21.88% 1.87% 100000 52000 88000 40.00% 47.66% 7.66% 100000 68000 92000 60.00% 62.50% 2.50% 100000 83999 95999 80.00% 80.47% 0.47% 100000 100000 100000 100.00% 100.00% 0.00% 1000000 360000 840000 20.00% 19.53% -0.47% 1000000 520000 880000 40.00% 40.62% 0.62% 1000000 680000 920000 60.00% 58.59% -1.41% 1000000 839999 959999 80.00% 75.78% -4.22% 1000000 1000000 1000000 100.00% 100.00% 0.00%","breadcrumbs":"Compaction » min-hash » Simulation","id":"25","title":"Simulation"},"26":{"body":"With min-hash we can find the best choice to compact. For every SSTable, calculate the Jaccard index of it and the overlapping SSTable at the lower level. Push down the one with the max Jaccard index. The space cost is negligible. Only 1KB more space for every SSTable. The time complexity is O(n), where n is the number of SSTable in the system. Because for every SSTable, there are about only k SSTable that have overlapping key range with it.where k is the level fanout.","breadcrumbs":"Compaction » min-hash » Optimize compaction with min-hash","id":"26","title":"Optimize compaction with min-hash"},"27":{"body":"Multiple SSTable are stored in a large file, the DataFile. DataFile only allocates or reclaims space by a fixed size: its allocation unit. There is one DataFile for each allocation unit. Assuming in openkv the allocation unit are 4MB and 16MB, then there are two DataFiles: df-4mb and df-16mb. Each DataFile has a corresponding bitmap for tracking allocated unit. The bitmap is part of the manifest bitmap-4mb:DataFile-4mb:bitmap-16mb:1SST01...00111100SST0SST0...","breadcrumbs":"Data File » DataFile","id":"27","title":"DataFile"},"28":{"body":"Find the first 0 in df-bitmap. This bitmap has to be indexed to speed up searching for the first 0. Flush and fsync SSTable data to DataFile. Flush and fsync bitmap in manifest .","breadcrumbs":"Data File » Commit a SSTable","id":"28","title":"Commit a SSTable"},"29":{"body":"Manifest in openkv itself is a tiny db with WAL of operations to the system and a snapshot. Snapshot: version: String data_file_bitmaps: { \"4mb\": Bitmap \"16mb\": Bitmap\n} spans: [ { start: String end: String vsstables: { 0: [VSST1, VSST2, ...] 1: [VSSTi, VSSTj, ...], } }, ...\n] separated_values: [ { start_value_id: String, end_value_id: String vsstables: { 0: [VSST1, VSST2, ...] 1: [VSSTi, VSSTj, ...], } }, ... ]","breadcrumbs":"Manifest » Manifest","id":"29","title":"Manifest"},"3":{"body":"Header is fix-sized and contains an SSTable format version etc.","breadcrumbs":"SSTable » Header","id":"3","title":"Header"},"4":{"body":"Metas stores configs of this SSTable, such as key types, value types, etc. E.g., a fix-sized key or value may use a type-specific store format. Fix-sized key does not need to store key-suffix in Records segment. TODO: prove it. Metas also stores the cardinality signature of all keys to optimize SSTable compaction.","breadcrumbs":"SSTable » Metas","id":"4","title":"Metas"},"5":{"body":"Index is a trie built from all keys stored in this SSTable, without single-branch tail. The leaf node in the trie stored the corresponding offset of a record in Records. It contains enough info to locate a present key in the Records segment. But there could be a false-positive for a key not in Records. For a given example of 3 key values: fantastice: 1\nfoo: 5\nfood: 3 The Index would be like this: faooffset for fantasticeooffset of foodoffset of food","breadcrumbs":"SSTable » Index","id":"5","title":"Index"},"6":{"body":"Index is preferred to reside in memory, while the Records is left on disk.","breadcrumbs":"SSTable » Caching","id":"6","title":"Caching"},"7":{"body":"Not all keys in the Index has a corresponding offset stored for it. 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By splitting LSM into several smaller ones, l becomes smaller and the write/read amplification will be reduced. Thus openkv organize its data in a way resembles to a two-level BTree: The btree root node is a array of all sub-LSM, sorted in key order. Each of the leaf nodes is a small LSM. L0L1L3L2L0L1L0L0(-oo, b]L2L1L0[b, e)L0[e, +oo)L2L1L0","breadcrumbs":"Internal Sharding » Sharding","id":"15","title":"Sharding"},"16":{"body":"Sub-LSM is a small LSM tree, with a limited number of levels.","breadcrumbs":"Internal Sharding » Sub-LSM","id":"16","title":"Sub-LSM"},"17":{"body":"A sub-LSM will be split if the level exceeds a threshold(e.g., 3). Two adjacent sub-LSM is merged into one if both of them becomes lower than 1/3 of the threshold.","breadcrumbs":"Internal Sharding » Split and Merge","id":"17","title":"Split and Merge"},"18":{"body":"Push a SSTable down and merge it with all overlapping SSTable at the next lower level. Leave only the record with the greatest seq when merging. When reaching the bottom level, i.e, level-0, a tombstone record can be removed for good.","breadcrumbs":"Compaction » Compaction","id":"18","title":"Compaction"},"19":{"body":"min-hash is a signature of all keys in a SSTable and is used to optimize the compaction. E.g., find out a pair of SSTable with most common keys.","breadcrumbs":"Compaction » min-hash » Min-hash","id":"19","title":"Min-hash"},"2":{"body":"A SSTable(solid-state table) is the same concept used in levelDB or rocksDB. The size of an SSTable can only be 4MB(for tombstone only SSTable) or 16MB(regular SSTable). The data layout inside an SSTable: HeaderMetasIndexRecordsChecksum","breadcrumbs":"SSTable » SSTable","id":"2","title":"SSTable"},"20":{"body":"Let U be a set and A and B be subsets of U, then the Jaccard index is defined to be the ratio of the number of elements of their intersection and the number of elements of their union: J(A,B)=∣A∪B∣∣A∩B∣. Let h be a hash function that maps the members of U to distinct integers, e.g., let h(x) = SHA1(x). For any set S, define H_min(S) to be the minimal integer(hash value) of members in S: H_min(S) = min({h(x) | x ∈ S}) Now, applying H_min to both A and B, and assuming no hash collisions, the probability that H_min(A) == H_min(B) is true is equal to the similarity J(A,B): Pr[ H_min(A) = H_min(B) ] = J(A,B)","breadcrumbs":"Compaction » min-hash » Jaccard similarity","id":"20","title":"Jaccard similarity"},"21":{"body":"Given two SSTable, the number of common keys can be calculated with: c=1+pp(∣A∣+∣B∣)","breadcrumbs":"Compaction » min-hash » Estimate the number of common keys","id":"21","title":"Estimate the number of common keys"},"22":{"body":"The probability can be estimiated with y/k, where k is the number of different hash functions and y is the number of hash functions hᵢ for which hᵢ(A) == hᵢ(B)","breadcrumbs":"Compaction » min-hash » Estimate the Probability","id":"22","title":"Estimate the Probability"},"23":{"body":"fn gen_sstable_signature(sstable: &SSTable, number_of_hashes: usize) -> Vec{ // Result signature let signature = Vec::with_capacity(number_of_hashes); // Distribute hash values to `k` buckets to simulate `k` hash functions. let buckets = Vec::with_capacity(number_of_hashes); for k in sstable.keys() { let h = SHA1(k) as u64; buckets[h%number_of_hashes].push(h); } for i in 0..number_of_hashes { signature[i] = min(buckets[i]); } signature\n}","breadcrumbs":"Compaction » min-hash » Generate signature for a SSTable","id":"23","title":"Generate signature for a SSTable"},"24":{"body":"fn calc_sig(a: &SSTable, b:&SSTable) -> f64 { let eq = 0.0; for i in 0..number_of_hashes: if a.signature[i] == a.signature[i] { eq += 1 } eq / number_of_hashes }","breadcrumbs":"Compaction » min-hash » Calculate similarity of two SSTable","id":"24","title":"Calculate similarity of two SSTable"},"25":{"body":"We provides a python script min-hash.py to estimate the accuracy of this algo. Config value Number of hash functions(buckets) 128 Hash value u64 Space cost sizeof(u64) * 128 = 1KB Actual vs Estimated: |A∪B| |A| |B| Actual (A∩B)/(A∪B)% Estimated% error% 1000 360 840 20.00% 21.88% 1.87% 1000 520 880 40.00% 38.28% -1.72% 1000 680 920 60.00% 60.94% 0.94% 1000 839 959 80.16% 78.91% -1.25% 1000 1000 1000 100.00% 100.00% 0.00% 10000 3600 8400 20.00% 15.62% -4.38% 10000 5200 8800 40.00% 35.16% -4.84% 10000 6800 9200 60.00% 60.94% 0.94% 10000 8399 9599 80.02% 85.16% 5.14% 10000 10000 10000 100.00% 100.00% 0.00% 100000 36000 84000 20.00% 21.88% 1.87% 100000 52000 88000 40.00% 47.66% 7.66% 100000 68000 92000 60.00% 62.50% 2.50% 100000 83999 95999 80.00% 80.47% 0.47% 100000 100000 100000 100.00% 100.00% 0.00% 1000000 360000 840000 20.00% 19.53% -0.47% 1000000 520000 880000 40.00% 40.62% 0.62% 1000000 680000 920000 60.00% 58.59% -1.41% 1000000 839999 959999 80.00% 75.78% -4.22% 1000000 1000000 1000000 100.00% 100.00% 0.00%","breadcrumbs":"Compaction » min-hash » Simulation","id":"25","title":"Simulation"},"26":{"body":"With min-hash we can find the best choice to compact. For every SSTable, calculate the Jaccard index of it and the overlapping SSTable at the lower level. Push down the one with the max Jaccard index. The space cost is negligible. Only 1KB more space for every SSTable. The time complexity is O(n), where n is the number of SSTable in the system. Because for every SSTable, there are about only k SSTable that have overlapping key range with it.where k is the level fanout.","breadcrumbs":"Compaction » min-hash » Optimize compaction with min-hash","id":"26","title":"Optimize compaction with min-hash"},"27":{"body":"Multiple SSTable are stored in a large file, the DataFile. DataFile only allocates or reclaims space by a fixed size: its allocation unit. There is one DataFile for each allocation unit. Assuming in openkv the allocation unit are 4MB and 16MB, then there are two DataFiles: df-4mb and df-16mb. Each DataFile has a corresponding bitmap for tracking allocated unit. The bitmap is part of the manifest bitmap-4mb:DataFile-4mb:bitmap-16mb:1SST01...00111100SST0SST0...","breadcrumbs":"Data File » DataFile","id":"27","title":"DataFile"},"28":{"body":"Find the first 0 in df-bitmap. This bitmap has to be indexed to speed up searching for the first 0. Flush and fsync SSTable data to DataFile. Flush and fsync bitmap in manifest .","breadcrumbs":"Data File » Commit a SSTable","id":"28","title":"Commit a SSTable"},"29":{"body":"Manifest in openkv itself is a tiny db with WAL of operations to the system and a snapshot. Snapshot: version data_file_bitmaps: { \"4mb\": Bitmap \"16mb\": Bitmap\n} spans: [\n{ start: String end: String vsst: { 0: [VS1, VS2, ...] 1: [VSi, VSj, ...], } } ]","breadcrumbs":"Manifest » Manifest","id":"29","title":"Manifest"},"3":{"body":"Header is fix-sized and contains an SSTable format version etc.","breadcrumbs":"SSTable » Header","id":"3","title":"Header"},"4":{"body":"Metas stores configs of this SSTable, such as key types, value types, etc. E.g., a fix-sized key or value may use a type-specific store format. Fix-sized key does not need to store key-suffix in Records segment. TODO: prove it. Metas also stores the cardinality signature of all keys to optimize SSTable compaction.","breadcrumbs":"SSTable » Metas","id":"4","title":"Metas"},"5":{"body":"Index is a trie built from all keys stored in this SSTable, without single-branch tail. The leaf node in the trie stored the corresponding offset of a record in Records. 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It can be considered as a BTreeMap. There is only one active MemTable for every openkv instance. Memtable is shared by all sub-LSM","breadcrumbs":"MemTable » MemTable","id":"0","title":"MemTable"},"1":{"body":"Flush MemTable to SSTable. If the MemTable becomes too large, flush one continous portion(span) into a sub-LSM. MemTable always flushes the biggest span, e.g., the one with most keys, unless there is a pressure to reclaim WAL space.","breadcrumbs":"MemTable » Flush","id":"1","title":"Flush"},"10":{"body":"One flush builds 2 SSTable: One of them contains all inserted or updated records, the Positive SSTable. The other one contains only deleted records, i.e., tomobstones: the Negative SSTable. Both has the same level and the same key range . In other word, we store updated recoreds and deleted records separately. Records part in P-SSTable:Records part in N-SSTable:key-suffixkey-suffix...key-suffixkey-suffix...seqseq...seqseq...valuevalue... By separating P/N records, it is possible to compact a N-SSTable down to reclaim space quickly. E.g., a Negative SSTable N1 can be pushed down and be merged with N2 and N3, without touching P1. Because to N1, P1 is transparent : N1 ∩ P1 = ø N2P2N1P1N3P3","breadcrumbs":"SSTable » Positive and Negative SSTable","id":"10","title":"Positive and Negative SSTable"},"11":{"body":"Search the key in the Index. If it matches a path in the trie, scan Records from the offset upto next offset to find the record. If the key-suffix also matches the search key, returns the value.","breadcrumbs":"SSTable » Reading a record","id":"11","title":"Reading a record"},"12":{"body":"Trie naturally compresses prefixes and an SSTable only stores a small range of keys thus the space cost is low enough. For a static trie, succinct data structure can be adopted to reduce the size of the trie. Our goal budget for a key is about several bytes. 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When reaching the bottom level, i.e, level-0, a tombstone record can be removed for good.","breadcrumbs":"Compaction » Compaction","id":"18","title":"Compaction"},"19":{"body":"min-hash is a signature of all keys in a SSTable and is used to optimize the compaction. E.g., find out a pair of SSTable with most common keys.","breadcrumbs":"Compaction » min-hash » Min-hash","id":"19","title":"Min-hash"},"2":{"body":"A SSTable(solid-state table) is the same concept used in levelDB or rocksDB. The size of an SSTable can only be 4MB(for tombstone only SSTable) or 16MB(regular SSTable). The data layout inside an SSTable: HeaderMetasIndexRecordsChecksum","breadcrumbs":"SSTable » SSTable","id":"2","title":"SSTable"},"20":{"body":"Let U be a set and A and B be subsets of U, then the Jaccard index is defined to be the ratio of the number of elements of their intersection and the number of elements of their union: J(A,B)=∣A∪B∣∣A∩B∣. 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For any set S, define H_min(S) to be the minimal integer(hash value) of members in S: H_min(S) = min({h(x) | x ∈ S}) Now, applying H_min to both A and B, and assuming no hash collisions, the probability that H_min(A) == H_min(B) is true is equal to the similarity J(A,B): Pr[ H_min(A) = H_min(B) ] = J(A,B)","breadcrumbs":"Compaction » min-hash » Jaccard similarity","id":"20","title":"Jaccard similarity"},"21":{"body":"Given two SSTable, the number of common keys can be calculated with: c=1+pp(∣A∣+∣B∣)","breadcrumbs":"Compaction » min-hash » Estimate the number of common keys","id":"21","title":"Estimate the number of common keys"},"22":{"body":"The probability can be estimiated with y/k, where k is the number of different hash functions and y is the number of hash functions hᵢ for which hᵢ(A) == hᵢ(B)","breadcrumbs":"Compaction » min-hash » Estimate the Probability","id":"22","title":"Estimate the Probability"},"23":{"body":"fn gen_sstable_signature(sstable: &SSTable, number_of_hashes: usize) -> Vec{ // Result signature let signature = Vec::with_capacity(number_of_hashes); // Distribute hash values to `k` buckets to simulate `k` hash functions. let buckets = Vec::with_capacity(number_of_hashes); for k in sstable.keys() { let h = SHA1(k) as u64; buckets[h%number_of_hashes].push(h); } for i in 0..number_of_hashes { signature[i] = min(buckets[i]); } signature\n}","breadcrumbs":"Compaction » min-hash » Generate signature for a SSTable","id":"23","title":"Generate signature for a SSTable"},"24":{"body":"fn calc_sig(a: &SSTable, b:&SSTable) -> f64 { let eq = 0.0; for i in 0..number_of_hashes: if a.signature[i] == a.signature[i] { eq += 1 } eq / number_of_hashes }","breadcrumbs":"Compaction » min-hash » Calculate similarity of two SSTable","id":"24","title":"Calculate similarity of two SSTable"},"25":{"body":"We provides a python script min-hash.py to estimate the accuracy of this algo. 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