Deterministic min-cost matching with delays

Yossi Azar*, Amit Jacob Fanani

*Corresponding author for this work

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


We consider the online Minimum-Cost Perfect Matching with Delays (MPMD) problem introduced by Emek et al. (STOC 2016), in which a general metric space is given, and requests are submitted in different times in this space by an adversary. The goal is to match requests, while minimizing the sum of distances between matched pairs in addition to the time intervals passed from the moment each request appeared until it is matched. In the online Minimum-Cost Bipartite Perfect Matching with Delays (MBPMD) problem introduced by Ashlagi et al. (APPROX/RANDOM 2017), each request is also associated with one of two classes, and requests can only be matched with requests of the other class. Previous algorithms for the problems mentioned above, include randomized O(log n) -competitive algorithms for known and finite metric spaces, n being the size of the metric space, and a deterministic O(m) -competitive algorithm, m being the number of requests. We introduce (formula presented) -competitive deterministic algorithms for both problems and for any fixed ɛ>0. In particular, for a small enough ɛ the competitive ratio becomes O(m 0.59 ). These are the first deterministic algorithms for the mentioned online matching problems, achieving a sub-linear competitive ratio. Our algorithms do not need to know the metric space in advance.

Original languageEnglish
Title of host publicationApproximation and Online Algorithms - 16th International Workshop, WAOA 2018, Revised Selected Papers
EditorsLeah Epstein, Thomas Erlebach
PublisherSpringer Verlag
Number of pages15
ISBN (Print)9783030046927
StatePublished - 2018
Event16th Workshop on Approximation and Online Algorithms, WAOA 2018 - Helsinki, Finland
Duration: 23 Aug 201824 Aug 2018

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11312 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference16th Workshop on Approximation and Online Algorithms, WAOA 2018


  • Bipartite matching
  • Competitive analysis
  • Delayed service
  • Matching
  • Online algorithm


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