Bloom Filters Burton Bloom (1970) Favorite Data Structure Underutilized Many Applications

Successful vs. unsuccessful search Quick fail method Checking file without accessing it

Basic idea Lo……ng Bit String 00010101010001010111010101010010000 n hash functions

24-bit Example H1(x) = H2(x) = H3(x) = 000000000000000000000000 0 8 16 23

What are the effects of size of filter and number of hash functions?

m – number of bits in filter k – number of records in file α - % of records in file to total population Pset = 1/m Punset = 1 – 1/m

For n transformations (hash functions) (1-1/m)n Pn.unset = (1-1/m)n For k records Pnk.unset = (1-1/m)nk Pnk.set = 1 - Pnk.unset Pnk.set = (1- (1-1/m)nk)

Pallset = (Pnk.set)n Pallset = [1- (1-1/m)nk]n Pfalse.drop = (1 – α)Pallset

Figure 7.1 (Gremillion, 1982)

Table II (Ramakrishna, 1989) hc,d(x) = ((cx + d) mod p) mod m, and H1 ={hc,d( ) | 0 < c < p, 0 ≤ d < p} 0 ≤ Key values ≤ p – 1 0 ≤ Hash values ≤ m - 1

k = number of transformations

How could Bloom Filters be used to eliminate duplicates? How could Bloom Filters be used with signature hashing?

Additions? Deletions? Counting Bloom Filters

More Applications Spell Checking Distributed Databases Web Page Caching Peer-to-peer Networks Increase Bandwidth in Cellular Networks

See A. Broder and M. Mitzenmacher, “Network Applications of Bloom Filters: A Survey,” in Fortieth Annual Allerton Conference on Communication, Control, and Computing, 2002.

Other Applications?