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International Workshop on Approximation and Online Algorithms

WAOA 2018: Approximation and Online Algorithms pp 21–35Cite as

Deterministic Min-Cost Matching with Delays

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11312))

Abstract

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 \(O\left( \log n\right) \)-competitive algorithms for known and finite metric spaces, n being the size of the metric space, and a deterministic \(O\left( m\right) \)-competitive algorithm, m being the number of requests.

We introduce \(O\left( m^{\log \left( \frac{3}{2}+\epsilon \right) }\right) \)-competitive deterministic algorithms for both problems and for any fixed \(\epsilon > 0\). In particular, for a small enough \(\epsilon \) the competitive ratio becomes \(O\left( m^{0.59}\right) \). 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.

Y. Azar—Supported in part by the Israel Science Foundation (grant No. 1506/16) and by the ICRC Blavatnik Fund.

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Authors and Affiliations

  1. School of Computer Science, Tel Aviv University, Tel Aviv, Israel

    Yossi Azar & Amit Jacob Fanani

Authors
  1. Yossi Azar
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  2. Amit Jacob Fanani
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Correspondence to Yossi Azar .

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Editors and Affiliations

  1. University of Haifa, Haifa, Israel

    Leah Epstein

  2. University of Leicester, Leicester, UK

    Thomas Erlebach

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Azar, Y., Jacob Fanani, A. (2018). Deterministic Min-Cost Matching with Delays. In: Epstein, L., Erlebach, T. (eds) Approximation and Online Algorithms. WAOA 2018. Lecture Notes in Computer Science(), vol 11312. Springer, Cham. https://doi.org/10.1007/978-3-030-04693-4_2

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  • DOI: https://doi.org/10.1007/978-3-030-04693-4_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-04692-7

  • Online ISBN: 978-3-030-04693-4

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