SearcharxivSearch

arXiv · 2304.12610

Fast Continuous Subgraph Matching over Streaming Graphs via Backtracking Reduction

Abstract

Streaming graphs are drawing increasing attention in both academic and industrial communities as many graphs in real applications evolve over time. Continuous subgraph matching (shorted as CSM) aims to report the incremental matches of a query graph in such streaming graphs. It involves two major steps, i.e., candidate maintenance and incremental match generation, to answer CSM. Throughout the course of continuous subgraph matching, incremental match generation backtracking over the search space dominates the total cost. However, most previous approaches focus on developing techniques for efficient candidate maintenance, while incremental match generation receives less attention despite its importance in CSM. Aiming to minimize the overall cost, we propose two techniques to reduce backtrackings in this paper. We present a cost-effective index CaLiG that yields tighter candidate maintenance, shrinking the search space of backtracking. In addition, we develop a novel incremental matching paradigm KSS that decomposes the query vertices into conditional kernel vertices and shell vertices. With the matches of kernel vertices, the incremental matches can be produced immediately by joining the candidates of shell vertices without any backtrackings. Benefiting from reduced backtrackings, the elapsed time of CSM decreases significantly. Extensive experiments over real graphs show that our method runs faster than the state-of-the-art algorithm orders of magnitude.

Explore related subjects

Keep this discovery

BibTeXRIS

Rongjian Yang, Zhijie Zhang, Weiguo Zheng, Jeffery Xu Yu. 2023-04-25. Fast Continuous Subgraph Matching over Streaming Graphs via Backtracking Reduction. https://arxiv.org/abs/2304.12610

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

KEEP EXPLORING

Related papers

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

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