Online matching: Haste makes waste!

Yuval Emek, Shay Kutten, Roger Wattenhofer

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


This paper studies a new online problem, referred to as mincost perfect matching with delays (MPMD), defined over a finite metric space (i.e., a complete graph with positive edge weights obeying the triangle inequality) M that is known to the algorithm in advance. Requests arrive in a continuous time online fashion at the points of M and should be served by matching them to each other. The algorithm is allowed to delay its request matching commitments, but this does not come for free: the total cost of the algorithm is the sum of metric distances between matched requests plus the sum of times each request waited since it arrived until it was matched. A randomized online MPMD algorithm is presented whose competitive ratio is O(log2 n + log Δ), where n is the number of points in M and Δ is its aspect ratio. The analysis is based on a machinery developed in the context of a new stochastic process that can be viewed as two interleaved Poisson processes; surprisingly, this new process captures precisely the behavior of our algorithm. A related problem in which the algorithm is allowed to clear any unmatched request at a fixed penalty is also addressed. It is suggested that the MPMD problem is merely the tip of the iceberg for a general framework of online problems with delayed service that captures many more natural problems.

Original languageEnglish
Title of host publicationSTOC 2016 - Proceedings of the 48th Annual ACM SIGACT Symposium on Theory of Computing
EditorsYishay Mansour, Daniel Wichs
Number of pages12
ISBN (Electronic)9781450341325
StatePublished - 19 Jun 2016
Event48th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2016 - Cambridge, United States
Duration: 19 Jun 201621 Jun 2016

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing


Conference48th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2016
Country/TerritoryUnited States


  • Alternate poisson process
  • Delayed service
  • Metric min-cost perfect matching
  • Online matching

All Science Journal Classification (ASJC) codes

  • Software


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