Optimization Online


Time-Indexed Relaxations for the Online Bipartite Matching Problem

Alfredo Torrico (atorrico3***at***gatech.edu)
Alejandro Toriello (atoriello***at***isye.gatech.edu)

Abstract: We study the i.i.d. online bipartite matching problem, a dynamic version of the classical model where one side of the bipartition is fixed and known in advance, while nodes from the other side appear one at a time as i.i.d. realizations of an underlying distribution, and must immediately be matched or discarded. We consider time-indexed relaxations of the set of achievable matching probabilities, introduce complete subgraph inequalities, show how they theoretically dominate inequalities from a lower-dimensional relaxation presented in previous work, and discuss when they are facet-defining. We finally present a computational study to demonstrate the empirical quality of the new relaxations and the heuristic policies they imply.

Keywords: Online optimization, bipartite matching, polyhedral relaxation, dynamic programming

Category 1: Other Topics (Dynamic Programming )


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Entry Submitted: 09/05/2017
Entry Accepted: 09/05/2017
Entry Last Modified: 02/19/2018

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