Online Stochastic Max-Weight Bipartite Matching: Beyond Prophet Inequalities

by   Christos Papadimitriou, et al.

The rich literature on online Bayesian selection problems has long focused on so-called prophet inequalities, which compare the gain of an online algorithm to that of a "prophet" who knows the future. An equally-natural, though significantly less well-studied benchmark is the optimum online algorithm, which may be omnipotent (i.e., computationally-unbounded), but not omniscient. What is the computational complexity of the optimum online? How well can a polynomial-time algorithm approximate it? Motivated by applications in ride hailing, we study the above questions for the online stochastic maximum-weight matching problem under vertex arrivals. This problem was recently introduced by Ezra, Feldman, Gravin and Tang (EC'20), who gave a 1/2-competitive algorithm for it. This is the best possible ratio, as this problem is a generalization of the original single-item prophet inequality. We present a polynomial-time algorithm which approximates optimal online within a factor of 0.51, beating the best-possible prophet inequality. At the core of our result are a new linear program formulation, an algorithm that tries to match the arriving vertices in two attempts, and an analysis that bounds the correlation resulting from the second attempts. In contrast, we show that it is PSPACE-hard to approximate this problem within some constant α < 1.



There are no comments yet.


page 1

page 2

page 3

page 4


Online Stochastic Matching, Poisson Arrivals, and the Natural Linear Program

We study the online stochastic matching problem. Consider a bipartite gr...

Prophet Inequalities for Matching with a Single Sample

We consider the prophet inequality problem for (not necessarily bipartit...

Popular matchings with weighted voters

In the Popular Matching problem, we are given a bipartite graph G = (A ∪...

Vertex-weighted Online Stochastic Matching with Patience Constraints

Online Bipartite Matching is a classic problem introduced by Karp, Vazir...

Online Graph Matching Problems with a Worst-Case Reassignment Budget

In the online bipartite matching with reassignments problem, an algorith...

Online Matching with Stochastic Rewards: Optimal Competitive Ratio via Path Based Formulation

The problem of online matching with stochastic rewards is a variant of t...

Online Hypergraph Matching with Delays

We study an online hypergraph matching problem with delays, motivated by...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.