Abstract

Abstract

Abstract
In a partitioned Bloom Filter (PBF) the bit vector is split into disjoint parts, one per hash function. Contrary to hardware designs, where they prevail, software implementations mostly ignore PBFs, considering them worse than standard Bloom filters (SBF), due to the slightly larger false positive rate (FPR). In this paper, by performing an in-depth analysis, first we show that the FPR advantage of SBFs is smaller than thought; more importantly, by deriving the per-element FPR, we show that SBFs have weak spots in the domain: elements that test as false positives much more frequently than expected. This is relevant in scenarios where an element is tested against many filters. Moreover, SBFs are prone to exhibit extremely weak spots if naive double hashing is used, something occurring in mainstream libraries. PBFs exhibit a uniform distribution of the FPR over the domain, with no weak spots, even using naive double hashing. Finally, we survey scenarios beyond set membership testing, identifying many advantages of having disjoint parts, in designs using SIMD techniques, for filter size reduction, test of set disjointness, and duplicate detection in streams. PBFs are better, and should replace SBFs, in general purpose libraries and as the base for novel designs.

Abstract

Abstract
Embedding CRDT counters has shown to be a challenging topic, since their introduction in Riak Maps. The desire for obliviousness, where all information about a counter is fully removed upon key removal, faces problems due to the possibility of concurrency between increments and key removals. Previous state-based proposals exhibit undesirable reset-wins semantics, which lead to losing increments, unsatisfactorily solved through manual generation management in the API. Previous operation-based approaches depend on causal stability, being prone to unbounded counter growth under network partitions. We introduce a novel embeddable operation-based CRDT counter which achieves both desirable observed-reset semantics and obliviousness upon resets. Moreover, it achieves this while merely requiring FIFO delivery, allowing a tradeoff between causal consistency and faster information propagation, being more robust under network partitions.