A Fully-dynamic Approximation Algorithm for Maximum Weight b-Matchings in Graphs

TL;DR

This paper introduces Dyn-b-suitor, a fully-dynamic algorithm for approximate maximum weight b-matchings in graphs, capable of efficiently updating solutions in response to graph changes, outperforming static methods significantly.

Contribution

It extends the static b-suitor algorithm to a dynamic setting, supporting both insertions and deletions while maintaining approximation guarantees.

Findings

Dynamic algorithm achieves up to 1000x speedup over static methods.

Supports both edge insertions and deletions without recomputing from scratch.

Significantly faster in real-world and generated graph experiments.

Abstract

Matching nodes in a graph G = (V, E) is a well-studied algorithmic problem with many applications. The b-matching problem is a generalizati on that allows to match a node with up to b neighbors. This allows more flexible connectivity patterns whenever vertices may have multiple associations. The algorithm b-suitor [Khan et al., SISC2016] is able to compute a (1/2)-approximation of a maximum weight b-matching in O(|E|) time. Since real-world graphs often change over time, fast dynamic methods for b-matching optimization are desirable. In this work, we propose Dyn-b-suitor, a dynamic algorithm for the weighted b-matching problem. As a non-trivial extension to the dynamic Suitor algorithm for 1-matchings [Angriman et al., JEA 2022], our approach computes (1/2)-approximate b-matchings by identifying and updating affected vertices without static recomputation. Our proposed algorithm is fully-dynamic, i. e., it supports both edge insertions and deletions, and we prove that it computes the same solution as its static counterpart. In extensive experiments on real-world benchmark graphs and generated instances, our dynamic algorithm yields significant savings compared to the sequential b-suitor, e. g., for batch updates with $10^3$ edges with an average acceleration factor of $10^3$. When comparing our sequential dynamic algorithm with the parallel (static) b-suitor on a 128-core machine, our dynamic algorithm is still $59$x to $10^4$ faster.