Supplementary material for “Lighter: fast and memory-efficient error correction without counting”

For a standard Bloom filter, each of the h hash functions could map item o to any element of the bit array. The bit array will often be very large, much larger than the processor cache. Thus, each probe into the bit array is likely to cause a cache miss. Putze et al [5] propose a blocked Bloom filter. Given a block size b, the first hash function H0(o) is used to select a size-b block of consecutive positions in the bit array. Then, H1(o), ..., Hh−1(o) map o onto elements of that block. When b is less than or equal to the size of a cache line, the h accesses will tend to cause only one or two cache misses, rather than approximately h cache misses. The drawback is that h and m must be somewhat larger to achieve the same false positive rate (FPR) as a corresponding standard Bloom filter. To estimate the FPR of the blocked Bloom filter, we can consider each of the possible m − b + 1 blocks. For the i-th block, the FPR within the block is (b′i/b) , where b′i is the number of bits set to 1 in block i. So the overall FPR is: