An Optimally-Competitive Algorithm for Maximum Online Perfect Bipartite Matching with i.i.d. Arrivals

We present an optimally-competitive algorithm for the problem of maximum online perfect bipartite matching with i.i.d. arrivals. In this problem, we are given a known set of workers, a distribution over job types, and non-negative utility weights for each pair of worker and job types. At each time s...

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Bibliographic Details
Published in:Theory of computing systems Vol. 64; no. 4; pp. 645 - 661
Main Authors: Chang, Minjun, Hochbaum, Dorit S., Spaen, Quico, Velednitsky, Mark
Format: Journal Article
Language:English
Published: New York Springer US 01.05.2020
Springer Nature B.V
Subjects:
Algorithms
Arrivals
Competition
Computer Science
Matching
Optimization
Special Issue on Approximation and Online Algorithms 2018
Theory of Computation
Transportation problem
Utilities
Competitive ratio
i.i.d. arrivals
Perfect matching
ISSN:1432-4350, 1433-0490
Online Access:Get full text
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Summary:We present an optimally-competitive algorithm for the problem of maximum online perfect bipartite matching with i.i.d. arrivals. In this problem, we are given a known set of workers, a distribution over job types, and non-negative utility weights for each pair of worker and job types. At each time step, a job is drawn i.i.d. from the distribution over job types. Upon arrival, the job must be irrevocably assigned to a worker and cannot be dropped. The goal is to maximize the expected sum of utilities after all jobs are assigned. We introduce Dispatch , a 0.5-competitive, randomized algorithm. We also prove that 0.5-competitive is the best possible. When a job arrives, Dispatch first selects a “preferred worker” and assigns the job to this worker if it is available. The preferred worker is determined based on an optimal solution to a fractional transportation problem. If the preferred worker is not available, Dispatch randomly selects a worker from the available workers.
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ISSN:1432-4350
1433-0490
DOI:10.1007/s00224-019-09947-7