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

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

3. Basic idea
Lo……ng Bit String
n hash functions

4. 24-bit Example H1(x) = H2(x) = H3(x) = 000000000000000000000000

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

6. 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

7. 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)

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

9. Figure 7.1 (Gremillion, 1982)

11. 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

12. k = number of transformations

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

14. Additions?
Deletions?
Counting Bloom Filters

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

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

17. Other Applications?