title: Stochastic matching problem.
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.
authors.affiliation: Physics Department and Center for Computational Sciences, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy.
authors.forename: F
authors.initials: F
authors.lastname: Altarelli
authors.forename: A
authors.initials: A
authors.lastname: Braunstein
authors.forename: A
authors.initials: A
authors.lastname: Ramezanpour
authors.forename: R
authors.initials: R
authors.lastname: Zecchina
mesh_terms: D000465:Algorithms; D001185:Artificial Intelligence; D003198:Computer Simulation; D017711:Nonlinear Dynamics; D009716:Numerical Analysis, Computer-Assisted; D013269:Stochastic Processes; D035501:Uncertainty