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The Popular Matching and Condensation Problems Under Matroid Constraints

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Combinatorial Optimization and Applications (COCOA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8881))

Abstract

In this paper, we first consider a matroid generalization of the popular matching problem (without ties) introduced by Abraham, Irving, Kavitha, and Mehlhorn, and give a polynomial-time algorithm for this problem. In the second half of this paper, we consider the problem of transforming a given instance of the popular matching problem (without ties) by deleting a minimum number of applicants so that it has a popular matching under matroid constraints. This problem is a matroid generalization of the popular condensation problem proposed by Wu, Lin, Wang, and Chao. By using the results in the first half, we give a polynomial-time algorithm for this problem.

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Notes

  1. 1.

    It should be noted that in the papers [1, 3, 4], the case where preference lists have ties was considered. It seems that to extend the results of this paper to the case where preference lists have ties is a non-trivial open problem.

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Acknowledgements

This work was supported by JSPS KAKENHI Grant Number 25730006. The author would like to thank anonymous referees for helpful comments on an earlier version of this paper.

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Authors and Affiliations

  1. Institute of Mathematics for Industry, Kyushu University, Fukuoka, Japan

    Naoyuki Kamiyama

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  1. Naoyuki Kamiyama
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Correspondence to Naoyuki Kamiyama .

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Editors and Affiliations

  1. Zhejiang Normal University, Jinhua, Zhejiang, China

    Zhao Zhang

  2. University of Texas, Tyler, Texas, USA

    Lidong Wu

  3. University of Texas, Dallas, Texas, USA

    Wen Xu

  4. University of Texas, Dallas, USA

    Ding-Zhu Du

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Kamiyama, N. (2014). The Popular Matching and Condensation Problems Under Matroid Constraints. In: Zhang, Z., Wu, L., Xu, W., Du, DZ. (eds) Combinatorial Optimization and Applications. COCOA 2014. Lecture Notes in Computer Science(), vol 8881. Springer, Cham. https://doi.org/10.1007/978-3-319-12691-3_53

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  • DOI: https://doi.org/10.1007/978-3-319-12691-3_53

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-12690-6

  • Online ISBN: 978-3-319-12691-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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