Bloom Filters and Count-Min Sketches Explained
Bloom Filters and Count-Min Sketches are essential data structures in computer science for efficient data querying and approximation algorithms. Bloom Filters help determine if an element is likely present in a set, while Count-Min Sketches estimate frequencies of elements in streams of data. These image-rich explanations provide insights into their functionalities, implementations, and use cases.
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Presentation Transcript
S1:3({fred flintstone}) h2 h3 h1 0 1 0 1 0 0 0 1 0 S1:3({ barney rubble }) h3 h2 h1 1 0 0 1 0 0 1 0 0 S1:3(({ fred flintstone , barney rubble }) 1 1 0 1 1 0 0 1 1 1 0 1
Bloom filters a variant split the bit vector into k ranges, one for each hash function 0 0 0 0 0 0 0 0 0 bf.contains( fred flintstore ): return AND of all hashed bits h3 h1 h2 1 1 0 1 1 0 0 1 1 1 0 bf.contains( pebbles ): h3 h2 h1 1 1 0 1 1 0 0 1 1 1 0 2
Bloom filters a variant split the bit vector into k ranges, one for each hash function 0 0 0 0 0 0 0 0 0 a false positive! bf.contains( pebbles ): h3 h2 h1 1 1 0 1 1 0 0 1 1 1 0 3
BLOOM FILTERS COUNT -MIN SKETCHES 4
Count-min sketches split a real vector into k ranges, one for each hash function 0 0 0 0 0 0 0 0 0 cm.inc( fred flintstone , 3): add the value to each hash location h3 h1 h2 0 3 0 3 0 0 0 3 0 cm.inc( barney rubble ,5): h3 h2 h1 5 3 0 8 8 0 0 5 5 3 0 5
Count-min sketches split a real vector into k ranges, one for each hash function 0 0 0 0 0 0 0 0 0 3 cm.get( fred flintstone ): take minwhen retrieving a value h3 h1 h2 5 3 0 8 8 0 0 5 5 3 0 5 cm.get( barney rubble): h3 h2 h1 5 3 0 8 8 0 0 5 5 3 0 6
Count-min sketches split a real vector into k ranges, one for each hash function value retrieved for s is ??? cm.add(s,??) has been called cm.get( barney rubble): h3 h2 h1 5 3 0 8 8 0 0 5 5 if T is sum of all ?? values for any s, then Prob(error > T?) < ? 3 0 cm.add( pebbles , 2): h3 h2 h1 7 3 0 10 10 0 0 5 5 5 0 7
Count-min sketches Equivalently, use a matrix, and each hash leads to a different row ? = 2/? cm.inc( fred flintstone , 3): d = log1/? 0 3 0 3 0 3 0 0 0 cm.inc( barney rubble ,5): 5 8 5 3 0 3 0 0 0 8
