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Strongly Stable Assignment

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Algorithms – ESA 2010 (ESA 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6347))

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Abstract

An instance of the stable assignment problem consists of a bipartite graph with arbitrary node and edge capacities, and arbitrary preference lists (allowing both ties and incomplete lists) over the set of neighbors. An assignment is strongly stable if there is no blocking pair where one member of the pair strictly prefers the other member to some partner in the current assignment, and the other weakly prefers the first to some partner in its current assignment.

We give a strongly polynomial time algorithm to determine the existence of a strongly stable assignment, and compute one if it exists. The central component of our algorithm is a generalization of the notion of the critical set in bipartite matchings to the critical subgraph in bipartite assignment; this generalization may be of independent interest.

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Author information

Authors and Affiliations

  1. School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore

    Ning Chen

  2. Yahoo! Research, Santa Clara, CA, USA

    Arpita Ghosh

Authors
  1. Ning Chen
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  2. Arpita Ghosh
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Computing Science, TU Eindhoven, Eindhoven, The Netherlands

    Mark de Berg

  2. Institute for Computer Science, J.W. Goethe University, 60325, Frankfurt/Main, Germany

    Ulrich Meyer

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© 2010 Springer-Verlag Berlin Heidelberg

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Chen, N., Ghosh, A. (2010). Strongly Stable Assignment. In: de Berg, M., Meyer, U. (eds) Algorithms – ESA 2010. ESA 2010. Lecture Notes in Computer Science, vol 6347. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15781-3_13

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  • DOI: https://doi.org/10.1007/978-3-642-15781-3_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15780-6

  • Online ISBN: 978-3-642-15781-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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