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Stable Matchings in Trees

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Computing and Combinatorics (COCOON 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10392))

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Abstract

The maximum stable matching problem (Max-SMP) and the minimum stable matching problem (Min-SMP) have been known to be NP-hard for subcubic bipartite graphs, while Max-SMP can be solved in polynomal time for a bipartite graph G with a bipartition (X, Y) such that \(\mathrm{deg}_{G}(v)\le 2\) for any \(v\in X\). This paper shows that both Max-SMP and Min-SMP can be solved in linear time for trees. This is the first polynomially solvable case for Min-SMP, as far as the authors know. We also consider some extensions to the case when G is a general/bipartite graph with edge weights.

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Acknowledgements

The research was partially supported by JSPS KAKENHI Grant Number 26330007.

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Authors and Affiliations

  1. Department of Information and Communications Engineering, Tokyo Institute of Technology, S3-57, Tokyo, 152-8550, Japan

    Satoshi Tayu & Shuichi Ueno

Authors
  1. Satoshi Tayu
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  2. Shuichi Ueno
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Correspondence to Satoshi Tayu .

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Editors and Affiliations

  1. Department of Computing, Hong Kong Polytechnic University, Hong Kong, China

    Yixin Cao

  2. Texas A&M University, College Station, Texas, USA

    Jianer Chen

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Tayu, S., Ueno, S. (2017). Stable Matchings in Trees. In: Cao, Y., Chen, J. (eds) Computing and Combinatorics. COCOON 2017. Lecture Notes in Computer Science(), vol 10392. Springer, Cham. https://doi.org/10.1007/978-3-319-62389-4_41

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  • DOI: https://doi.org/10.1007/978-3-319-62389-4_41

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-62388-7

  • Online ISBN: 978-3-319-62389-4

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