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Approximating Multistage Matching Problems

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Combinatorial Algorithms (IWOCA 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12757))

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Abstract

In multistage perfect matching problems, we are given a sequence of graphs on the same vertex set and are asked to find a sequence of perfect matchings, corresponding to the sequence of graphs, such that consecutive matchings are as similar as possible. More precisely, we aim to maximize the intersections, or minimize the unions between consecutive matchings.

We show that these problems are NP-hard even in very restricted scenarios. As our main contribution, we present the first non-trivial approximation algorithms for these problems: On the one hand, we devise a tight approximation on graph sequences of length two (2-stage graphs). On the other hand, we propose several general methods to deduce multistage approximations from blackbox approximations on 2-stage graphs.

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Authors and Affiliations

  1. Theoretical Computer Science, Osnabrück University, Osnabrück, Germany

    Markus Chimani, Niklas Troost & Tilo Wiedera

Authors
  1. Markus Chimani
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  2. Niklas Troost
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  3. Tilo Wiedera
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Corresponding author

Correspondence to Niklas Troost .

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Editors and Affiliations

  1. University of Ottawa, Ottawa, ON, Canada

    Paola Flocchini

  2. University of Ottawa, Ottawa, ON, Canada

    Lucia Moura

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Chimani, M., Troost, N., Wiedera, T. (2021). Approximating Multistage Matching Problems. In: Flocchini, P., Moura, L. (eds) Combinatorial Algorithms. IWOCA 2021. Lecture Notes in Computer Science(), vol 12757. Springer, Cham. https://doi.org/10.1007/978-3-030-79987-8_39

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  • DOI: https://doi.org/10.1007/978-3-030-79987-8_39

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-79986-1

  • Online ISBN: 978-3-030-79987-8

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