AccessEfficient Balanced Bloom Filters Motivation Classical Bloom Filters

Access-Efficient Balanced Bloom Filters Motivation § Classical Bloom Filters need a significant number of memory accesses. § Bloom Filter with 30 bits per element 30・ln 2 ≈ 21 memory accesses. § Each memory access may be to a distinct memory block Energy- and cache-inefficient. § Blocked Bloom Filter [Putze et al. ]: Choose a memory block first; then local Bloom Filter within each block. § Might cause imbalance between memory blocks Efficient, but poor false positive rate. Our Proposal • Balance the load between the blocks using multiple hash functions. • Upon a query, an element might be found in more than one bucket. • Objective: minimize the average number of buckets needed to be checked, ensuring the optimal balancing between the buckets. • In addition, restrict the worst-case number of buckets need to be checked. • Utilize an overflow list (in CAM) of size to mitigate such extreme situations. Lower Bound – Basic Idea Model • - The occupancy of bucket , given buckets, element, and a balancing scheme (random variable). • - General cost function mapping bucket occupancy to its cost. • Overall balancing quality: • Given and , we consider an initial insertion of distinct elements. • Then, we remove elements from the most occupied buckets, until exactly elements are left. • Looks like “pushed-back” Poisson distribution. • The specific cost function for Bloom filter is FPR: • Valid for any convex cost function Upper Bounds Example: The Balanced Bloom Filter • Based on Multi-level Hash Tables (MHT). • Upon a query, up to hash functions are • Using 3 subtables of (4, 2 and 1 memory used one by one, where the next hash is blocks). used only if the occupancy of the mapped • In each memory block, 2 bits are saved for bucket exceeds some threshold. a counter so bucket occupancy can be • More specifically, the following schemes determined. are used: • A simple scheme (using only a single hash function). • A sequential scheme, using hash functions with uniform distribution. • A Mutli-level Hash-Table scheme (MHT), divides the memory into subtables with a single hash function for each subtable. . Evaluation • Two orders of magnitude FPR improvement upon Blocked Bloom Filter, for a memory block size of 256 bits MHT with an overflow list size 0. 49% and only 1. 2 memory accesses per element. • All results were confirmed using real-life traces.