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A Matroid Generalization of the Stable Matching Polytope

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Integer Programming and Combinatorial Optimization (IPCO 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2081))

Abstract

By solving a constrained matroid intersection problem, we give a matroid generalization of the stable marriage theorem of Gale and Shapley.We describe the related matroid-kernel polytope, an extension of the stable matching polytope. Linear conditions of the characterizations resemble to the ones that describe the matroid intersection polytope.

Research was done as part of the author’s PhD studies at the Centrum voor Wiskunde en Informatica (CWI), POB 94079, NL-1090GB, Amsterdam and it was supported by the Netherlands Organization for Scientific Research (NWO) and by OTKA T 029772.

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Author information

Authors and Affiliations

  1. Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, 127, H-1364, Budapest, Hungary

    Tamás Fleiner

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  1. Tamás Fleiner
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Editors and Affiliations

  1. Instituut voor Informatica en Informatiekunde, Universiteit Utrecht, Padualaan 14, 3584, CH Utrecht, The Netherlands

    Karen Aardal

  2. CWI, Kruislaan 413, 1098, SJ Amsterdam, The Netherlands

    Bert Gerards

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© 2001 Springer-Verlag Berlin Heidelberg

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Fleiner, T. (2001). A Matroid Generalization of the Stable Matching Polytope. In: Aardal, K., Gerards, B. (eds) Integer Programming and Combinatorial Optimization. IPCO 2001. Lecture Notes in Computer Science, vol 2081. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45535-3_9

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  • DOI: https://doi.org/10.1007/3-540-45535-3_9

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42225-9

  • Online ISBN: 978-3-540-45535-6

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