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A Polyhedral Approach to Online Bipartite Matching

Alfredo Torrico (atorrico3***at***gatech.edu)
Shabbir Ahmed (sahmed***at***isye.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 a uniform distribution, and must immediately be matched or discarded. We consider various relaxations of the polyhedral set of achievable matching probabilities, introduce valid inequalities, and discuss when they are facet-defining. We also show how several of these relaxations correspond to ranking policies and their time-dependent generalizations. We finally present a computational study of these relaxations and policies to determine their empirical performance.

Keywords: online matching, dynamic program, polyhedral relaxation

Category 1: Combinatorial Optimization (Polyhedra )

Category 2: Other Topics (Dynamic Programming )

Citation: Stewart School of Industrial and Systems Engineering, April, 2016

Download: [PDF]

Entry Submitted: 04/11/2016
Entry Accepted: 04/11/2016
Entry Last Modified: 07/12/2017

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