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International Conference on Algorithmic Decision Theory

ADT 2017: Algorithmic Decision Theory pp 315–330Cite as

Stable Roommate with Narcissistic, Single-Peaked, and Single-Crossing Preferences

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10576))

Abstract

The classical Stable Roommate problem asks whether it is possible to pair up an even number of agents such that no two non-paired agents prefer to be with each other rather than with their assigned partners. We investigate Stable Roommate with complete (i.e. every agent can be matched with every other agent) or incomplete preferences, with ties (i.e. two agents are considered of equal value to some agent) or without ties. It is known that in general allowing ties makes the problem NP-complete. We provide algorithms for Stable Roommate that are, compared to those in the literature, more efficient when the input preferences are complete and have some structural property, such as being narcissistic, single-peaked, and single-crossing. However, when the preferences are incomplete and have ties, we show that being single-peaked and single-crossing does not reduce the computational complexity—Stable Roommate remains NP-complete.

R. Bredereck was on postdoctoral leave at the University of Oxford (GB) from September 2016 to September 2017, supported by the DFG fellowship BR 5207/2.

J. Chen was partly supported by the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreement number 631163.11 and Israel Science Foundation (grant no. 551145/14).

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Notes

  1. 1.

    For technical reasons, an agent may find itself acceptable, which means that \(\{i\} \subseteq V_i\).

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Author information

Authors and Affiliations

  1. TU Berlin, Berlin, Germany

    Robert Bredereck, Jiehua Chen, Ugo Paavo Finnendahl & Rolf Niedermeier

  2. Ben-Gurion University of the Negev, Beersheba, Israel

    Jiehua Chen

Authors
  1. Robert Bredereck
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  2. Jiehua Chen
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  3. Ugo Paavo Finnendahl
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  4. Rolf Niedermeier
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Corresponding author

Correspondence to Jiehua Chen .

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Editors and Affiliations

  1. Heinrich Heine University, Düsseldorf, Germany

    Jörg Rothe

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Bredereck, R., Chen, J., Finnendahl, U.P., Niedermeier, R. (2017). Stable Roommate with Narcissistic, Single-Peaked, and Single-Crossing Preferences. In: Rothe, J. (eds) Algorithmic Decision Theory. ADT 2017. Lecture Notes in Computer Science(), vol 10576. Springer, Cham. https://doi.org/10.1007/978-3-319-67504-6_22

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  • DOI: https://doi.org/10.1007/978-3-319-67504-6_22

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-67503-9

  • Online ISBN: 978-3-319-67504-6

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