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A Match in Time Saves Nine: Deterministic Online Matching with Delays

  • Marcin BienkowskiEmail author
  • Artur Kraska
  • Paweł Schmidt
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10787)

Abstract

We consider the problem of online Min-cost Perfect Matching with Delays (MPMD) introduced by Emek et al. (STOC 2016). In this problem, an even number of requests appear in a metric space at different times and the goal of an online algorithm is to match them in pairs. In contrast to traditional online matching problems, in MPMD all requests appear online and an algorithm can match any pair of requests, but such decision may be delayed (e.g., to find a better match). The cost is the sum of matching distances and the introduced delays.

We present the first deterministic online algorithm for this problem. Its competitive ratio is \(O(m^{\log _2 5.5})\) \( = O(m^{2.46})\), where 2m is the number of requests. In particular, the bound does not depend on other parameters of the metric, such as its aspect ratio. Unlike previous (randomized) solutions for the MPMD problem, our algorithm does not need to know the metric space in advance and it does not require the space to be finite.

Keywords

Online matching Delays Rent-or-buy Competitive analysis 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Computer ScienceUniversity of WrocławWrocławPoland

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