Beating $(1-1/e)$-Approximation for Weighted Stochastic Matching

TL;DR

This paper presents an improved algorithm for the weighted stochastic matching problem that surpasses the long-standing $(1-1/e)$ approximation barrier, achieving a better approximation ratio in bipartite graphs.

Contribution

It introduces a novel algorithm that improves the approximation ratio beyond $(1-1/e)$ for weighted stochastic matching in bipartite graphs.

Findings

Achieves a $(1-1/e+ ext{constant})$-approximation, breaking the previous bound.

Provides theoretical proof of surpassing the $(1-1/e)$ approximation barrier.

Applicable to bipartite graphs with potential for broader impact.

Abstract

In the stochastic weighted matching problem, the goal is to find a large-weight matching of a graph when we are uncertain about the existence of its edges. In particular, each edge $e$ has a known weight $w_e$ but is realized independently with some probability $p_e$. The algorithm may query an edge to see whether it is realized. We consider the well-studied query commit version of the problem, in which any queried edge that happens to be realized must be included in the solution. Gamlath, Kale, and Svensson showed that when the input graph is bipartite, the problem admits a $(1-1/e)$-approximation. In this paper, we give an algorithm that for an absolute constant $\delta > 0.0014$ obtains a $(1-1/e+\delta)$-approximation, therefore breaking this prevalent bound.