Improved Competitive Ratio for Edge-Weighted Online Stochastic Matching

TL;DR

This paper introduces the Evolving Suggested Matching algorithm, improving the competitive ratio for edge-weighted online stochastic matching from 0.645 to 0.650, advancing the efficiency of online matching algorithms.

Contribution

The paper presents the Evolving Suggested Matching algorithm, achieving a higher competitive ratio for the problem than previous algorithms.

Findings

Achieves a competitive ratio of 0.650 for the problem.

Improves upon the previous best ratio of 0.645.

Provides a new algorithm with better theoretical guarantees.

Abstract

We consider the edge-weighted online stochastic matching problem, in which an edge-weighted bipartite graph G=(I\cup J, E) with offline vertices J and online vertex types I is given. The online vertices have types sampled from I with probability proportional to the arrival rates of online vertex types. The online algorithm must make immediate and irrevocable matching decisions with the objective of maximizing the total weight of the matching. For the problem with general arrival rates, Feldman et al. (FOCS 2009) proposed the Suggested Matching algorithm and showed that it achieves a competitive ratio of 1-1/e \approx 0.632. The ratio has recently been improved to 0.645 by Yan (2022), who proposed the Multistage Suggested Matching (MSM) algorithm. In this paper, we propose the Evolving Suggested Matching (ESM) algorithm, and show that it achieves a competitive ratio of 0.650.