Online Matching with General Arrivals

The online matching problem was introduced by Karp, Vazirani and Vazirani nearly three decades ago. In that seminal work, they studied this problem in bipartite graphs with vertices arriving only on one side, and presented optimal deterministic and randomized algorithms for this setting. In comparis...

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Bibliographic Details
Published in2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS) pp. 26 - 37
Main Authors Gamlath, Buddhima, Kapralov, Michael, Maggiori, Andreas, Svensson, Ola, Wajc, David
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.11.2019
Subjects
Bipartite graph
Computer science
edge arrivals
general vertex arrivals
Mathematical model
online algorithms
online matching
Optimization
Stochastic processes
Uncertainty
Upper bound
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Summary:The online matching problem was introduced by Karp, Vazirani and Vazirani nearly three decades ago. In that seminal work, they studied this problem in bipartite graphs with vertices arriving only on one side, and presented optimal deterministic and randomized algorithms for this setting. In comparison, more general arrival models, such as edge arrivals and general vertex arrivals, have proven more challenging and positive results are known only for various relaxations of the problem. In particular, even the basic question of whether randomization allows one to beat the trivially-optimal deterministic competitive ratio of 1/2 for either of these models was open. In this paper, we resolve this question for both these natural arrival models, and show the following.1) For edge arrivals, randomization does not help - no randomized algorithm is better than 1/2 competitive. 2)For general vertex arrivals, randomization helps - there exists a randomized (1/2+Ω(1)) -competitive online matching algorithm.
ISSN:2575-8454
DOI:10.1109/FOCS.2019.00011