The stochastic matching problem

TL;DR

This paper introduces an efficient method combining survey propagation and cavity method to solve stochastic matching problems, outperforming existing methods and applicable to various optimization under uncertainty scenarios.

Contribution

The paper presents a novel approach that effectively addresses stochastic matching problems by integrating survey propagation and cavity method techniques.

Findings

Method outperforms state-of-the-art algorithms.

Effective across the full parameter range.

Analyzed phase diagram and compared with bounds.

Abstract

The matching problem plays a basic role in combinatorial optimization and in statistical mechanics. In its stochastic variants, optimization decisions have to be taken given only some probabilistic information about the instance. While the deterministic case can be solved in polynomial time, stochastic variants are worst-case intractable. We propose an efficient method to solve stochastic matching problems which combines some features of the survey propagation equations and of the cavity method. We test it on random bipartite graphs, for which we analyze the phase diagram and compare the results with exact bounds. Our approach is shown numerically to be effective on the full range of parameters, and to outperform state-of-the-art methods. Finally we discuss how the method can be generalized to other problems of optimization under uncertainty.