Multiple Set Matching and Pre-Filtering with Bloom Multifilters

Francesco Concas; Pengfei Xu; Mohammad A. Hoque; Jiaheng Lu; Sasu Tarkoma

Home/Archive/arXiv

arXiv · 1901.01825

Multiple Set Matching and Pre-Filtering with Bloom Multifilters

Francesco Concas·Pengfei Xu·Mohammad A. Hoque·Jiaheng Lu·Sasu Tarkoma

View original source ↗Read source document ↗Export metadata ↓

Abstract

Bloom filter is a space-efficient probabilistic data structure for checking elements' membership in a set. Given multiple sets, however, a standard Bloom filter is not sufficient when looking for the items to which an element or a set of input elements belong to. In this article, we solve multiple set matching problem by proposing two efficient Bloom Multifilters called Bloom Matrix and Bloom Vector. Both of them are space efficient and answer queries with a set of identifiers for multiple set matching problems. We show that the space efficiency can be optimized further according to the distribution of labels among multiple sets: Uniform and Zipf. While both of them are space efficient, Bloom Vector can efficiently exploit Zipf distribution of data for further space reduction. Our results also highlight that basic ADD and LOOKUP operations on Bloom Matrix are faster than on Bloom Vector. However, Bloom Matrix does not meet the theoretical false positive rate of less than $10^{-2}$ for LOOKUP operations if the represented data or the labels are not uniformly distributed among the multiple sets. Consequently, we introduce \textit{Bloom Test} which uses Bloom Matrix as the pre-filter structure to determine which structure is suitable for improved performance with an arbitrary input dataset.

Explore related subjects

cs.DS

Keep this discovery

BibTeX RIS

Francesco Concas, Pengfei Xu, Mohammad A. Hoque, Jiaheng Lu, Sasu Tarkoma. 2019-01-07. Multiple Set Matching and Pre-Filtering with Bloom Multifilters. https://arxiv.org/abs/1901.01825

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Quasi-Monte Carlo Beyond Hardy-Krause II: $(1 + \varepsilon)n$ Samples Suffice

Numerical integration studies how well one can estimate the integral of a function $f$ over $[0,1)^d$ using $n$ sample points. The two classical methods, Monte Carlo (MC) and quasi-Monte Carlo (QMC), have complementary strengths and weaknesses, and a fundamental question is to design an approach that combines the benefits of both. Recently, building on the transference principle in discrepancy theory, Bansal and Jiang~\cite{BJ25a} gave a randomized QMC method that bridges MC and QMC guarantees using only i.i.d.\ samples. Their method also goes beyond the classical Koksma--Hlawka inequality: it achieves integration error $\widetilde{O}_d(\sigma_{\mathsf{SO}}(f)/n)$, where the smoothed-out variation $\sigma_{\mathsf{SO}}(f)$ can be substantially smaller than the Hardy--Krause variation that governs the classical bound. However, their algorithm requires $n^2$ i.i.d.\ samples as input, and this quadratic blowup is inherent to any method based on the transference principle. In this work, we bypass the quadratic blowup: for any constant $\varepsilon > 0$, we show that $(1+\varepsilon)n$ i.i.d.\ samples suffice to both obtain the beyond-Hardy--Krause guarantee of~\cite{BJ25a}, resolving an open problem posed there, and to produce low-discrepancy point sequences. Our algorithms are variants of the online Haar-thinning method of Dwivedi, Feldheim, Gurel-Gurevich, and Ramdas~\cite{DFG+19}.

cs.DS↗

arXiv2026

A deterministic $(1+\varepsilon)^n$ approximation for the permanent of a nonnegative matrix

For every fixed $0<\varepsilon\le1$, we give a deterministic strongly polynomial algorithm that, given a nonnegative matrix $A\in\mathbb{R}_{\ge0}^{n\times n}$, returns $Q$ satisfying $\operatorname{per} A\le Q\le(1+\varepsilon)^n\operatorname{per} A$.

cs.DS↗

arXiv2026

Single-Exponential Algorithms and a Polynomial Kernel for Strong Connectivity Augmentation

Strong Connectivity Augmentation (SCA) asks whether a directed acyclic graph can be made strongly connected by adding at most $k$ prescribed links whose total weight is within a given budget. Klinkby, Misra, and Saurabh (SODA 2021) gave an $O^*(2^{O(k\log k)})$-time algorithm and asked whether the problem admits a single-exponential parameterized algorithm and a polynomial kernel. We answer both questions affirmatively: SCA can be solved in $O^*(9^k)$ time and admits a polynomial kernel with $O(k^4)$ vertices and $O(k^{16})$ bits. For unweighted SCA, we obtain $O^*(4^k)$ time and a kernel with $O(k^3)$ vertices. Our algorithms are based on a particularly simple reduction to Strongly Connected Spanning Subgraph with two edge costs.

cs.DS↗