General Graphs are Easier than Bipartite Graphs: Tight Bounds for Secretary Matching

Tomer Ezra, Michal Feldman, Nick Gravin, Zhihao Gavin Tang

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Online algorithms for secretary matching in bipartite weighted graphs have been studied extensively in recent years. We generalize this study to secretary matching in general weighted graphs, for both vertex and edge arrival models. Under vertex arrival, vertices arrive online in a uniformly random order; upon the arrival of a vertex v, the weights of edges from v to all previously arriving vertices are revealed, and the algorithm decides which of these edges, if any, to include in the matching. We provide a tight 5/12-competitive algorithm for this setting. Interestingly, it outperforms the best possible algorithm for secretary matching in bipartite graphs with 1-sided arrival, which cannot be better than 1/e-competitive. Under edge arrival, edges arrive online in a uniformly random order; upon the arrival of an edge e, its weight is revealed, and the algorithm decides whether to include it in the matching or not. For this setting we provide a 1/4-competitive algorithm, which improves upon the state of the art bound.

Original languageEnglish
Title of host publicationEC 2022 - Proceedings of the 23rd ACM Conference on Economics and Computation
PublisherAssociation for Computing Machinery, Inc
Pages1148-1177
Number of pages30
ISBN (Electronic)9781450391504
DOIs
StatePublished - 12 Jul 2022
Event23rd ACM Conference on Economics and Computation, EC 2022 - Boulder, United States
Duration: 11 Jul 202215 Jul 2022

Publication series

NameEC 2022 - Proceedings of the 23rd ACM Conference on Economics and Computation

Conference

Conference23rd ACM Conference on Economics and Computation, EC 2022
Country/TerritoryUnited States
CityBoulder
Period11/07/2215/07/22

Keywords

  • online matching
  • secretary problem

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