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Bloom filter

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Bloom filter

  1. 1. Bloom Filter YHD Search Sharing 2013-04-23
  2. 2. Outline ● Interview questions ● Bloom Filter – Data structure – Probability of false positives – Set properties ● Application – Cache sharing : squid – Speed up data access : Hbase – ID Mapping : zoie ● Materials
  3. 3. Interview questions ● Crawler – Billions web pages – How to keep track crawled urls ● Straggler Detection – You are manning the security desk of a large building – Everyone checks in or checks out with their id – At the end of day, identify the few stragglers left in the building
  4. 4. Data structure ● Data structure – Init : a bit array of m bits, all set to 0 – Add an element ● K hash function to get K array positions ● Set the bits at all these positions to 1 ● Query an element (test whether it's in the set) – K hash function to get K array positions – If any position are 0, not in the set – If all are 1, probabilistic in the set
  5. 5. Probability of false positives ● 1 hash function 0 0 0 0 0 0 0 1 0 00 0 0 1 0 0 0 0 0 0 0 0 0 0 p( A[i]=1∣hash[ x1 ,…, xn])=1−(1− 1 m ) n p(hash[ x1]=i)= 1 m p( A[i]=0∣hash[x1])=1− 1 m p( A[i]=0∣hash[x1 ,…,xn])=(1− 1 m ) n p( A[i]=1)=1−(1− 1 m ) n ≃1−e −n/m lim x→ ∞ (1− 1 x ) −x =e
  6. 6. Probability of false positives ● 1 hash function 0 0 0 0 0 0 0 1 0 00 0 0 1 0 0 0 0 0 0 0 0 0 0 p( A[ H ( y)]=1∣y∉S)= (number of 1) m 2/23 p( A[i]=1)=1−e −n/m Given E(number of 1)=m⋅(1−e −n/m ) p( A[ H ( y)]=1∣y∉S)=(1−e −n/m )
  7. 7. Probability of false positives ● K hash function : repeat for k times 0 0 0 0 0 0 0 1 0 00 0 0 1 0 0 0 0 0 0 0 0 0 0 p( A[ H ( y)]=1∣y∉S)= (number of 1) m p( A[i]=1)=1−e −n/m Given E(number of 1)=m⋅(1−e −n/m ) p( A[ H ( y)]=1∣y∉S)=(1−e −n/m ) p( A[ H ( y)]=1∣y∉S)=( number of 1 m ) k p( A[i]=1)=1−(1− 1 m ) kn ≃1−e −kn/m E(number of 1)=m⋅(1−e −kn/m ) p( A[ H ( y)]=1∣y∉S)=(1−e −kn/m ) k
  8. 8. Probability of false positives ● Minimal Probability of false positives p( A[ H ( y)]=1∣y∉S)=(1−e −kn/m ) k f =(1−e −kn/m ) k f =e k∗ln (1−e −kn/m ) Minimal f, then minimal g g=k∗ln (1−e −kn/m ) p=e −kn/m Given g=− m n ln( p)∗ln(1−p) Minimal(f )=( 1 2 ) k p= 1 2 e −kn/m = 1 2 is the probability than any specific bit is still 0 half-full Bloom filter array
  9. 9. Probability of false positives ● examples k=ln2 m n m/n k k=1 k=2 k=3 k=4 k=5 2 1.39 0.393 0.400 3 2.08 0.283 0.237 0.253 4 2.77 0.221 0.155 0.147 0.160 5 3.46 0.181 0.109 0.092 0.092 0.101 6 4.16 0.154 0.0804 0.0609 0.0561 0.0578 7 4.85 0.133 0.0618 0.0423 0.0359 0.0347 8 5.55 0.118 0.0489 0.0306 0.024 0.0217
  10. 10. Set properties ● Union (bitwise OR) – same as the Bloom filter created from scratch using the union of the two sets. ● Intersection (AND operations) – the false positive probability in the resulting Bloom filter is at most the false-positive probability in one of the constituent Bloom filters, but may be larger than the false positive probability in the Bloom filter created from scratch using the intersection of the two sets
  11. 11. Squid : Cache Digests
  12. 12. Squid : Cache Digests
  13. 13. Squid : Cache Digests
  14. 14. Squid : Cache Digests
  15. 15. Squid : Cache Digests ● False positive: – Proxy A thinks Proxy B has URL U cached. A asks for cached U, B responds back with “no”, A goes to actual website.
  16. 16. HBase :architecture
  17. 17. Hbase :HFile format ● (Not including Bloom Filter)
  18. 18. HBase : Query optimization ● Bloom Filter – As meta store of HFile – used to determine if a given key is in that store file ● Characteristics – Know n total KV count (N), but actual count can often be much lower – HFile.insert (and hence, BloomFilter.add) commands are done in lexicographically increasing order 4000 10000 5000 9001
  19. 19. Application : Zoie ● Long[] uidArray – Add element – Query element int h = (int) ((uid >>> 32) ^ uid) * MIXER; long bits = _filter[h & _mask]; bits |= ((1L << (h >>> 26))); bits |= ((1L << ((h >> 20) & 0x3F))); _filter[h & _mask] = bits; final int h = (int) ((uid >>> 32) ^ uid) * MIXER; final int p = h & _mask; // check the filter final long bits = _filter[p]; if ((bits & (1L << (h >>> 26))) == 0 || (bits & (1L << ((h >> 20) & 0x3F))) == 0) return -1;
  20. 20. Materials ● http://www.cs.jhu.edu/~fabian/courses/CS600.6 24/slides/bloomslides.pdf ● Google tech talk, bloom filtering ● http://www.slideshare.net/jaxlondon2012/intro -to-hbase-lars-george ● https://issues.apache.org/jira/secure/attachme nt/12444007/Bloom_Filters_in_HBase.pdf

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