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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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
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Abstract	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.
AbstractList	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. 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.
Author	Chang, Minjun Spaen, Quico Velednitsky, Mark Hochbaum, Dorit S.
Author_xml	– sequence: 1 givenname: Minjun surname: Chang fullname: Chang, Minjun organization: Fuqua School of Business, Duke University – sequence: 2 givenname: Dorit S. surname: Hochbaum fullname: Hochbaum, Dorit S. organization: Department of Industrial Engineering and Operations Research, University of California – sequence: 3 givenname: Quico surname: Spaen fullname: Spaen, Quico organization: Department of Industrial Engineering and Operations Research, University of California – sequence: 4 givenname: Mark orcidid: 0000-0003-1176-5159 surname: Velednitsky fullname: Velednitsky, Mark email: marvel@berkeley.edu organization: Department of Industrial Engineering and Operations Research, University of California
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Title	An Optimally-Competitive Algorithm for Maximum Online Perfect Bipartite Matching with i.i.d. Arrivals
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