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A Fine-Grained View on Stable Many-To-One Matching Problems with Lower and Upper Quotas

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Web and Internet Economics (WINE 2020)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 12495))

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Abstract

In the Hospital Residents problem with lower and upper quotas (HR- \({Q}_{L}^{U}\)), the goal is to find a stable matching of residents to hospitals where the number of residents matched to a hospital is either between its lower and upper quota or zero [Biró et al., TCS 2010]. We analyze this problem from a parameterized perspective using several natural parameters such as the number of hospitals and the number of residents. Moreover, we present a polynomial-time algorithm that finds a stable matching if it exists on instances with maximum lower quota two. Alongside HR- \({Q}_{L}^{U}\), we also consider two closely related models of independent interest, namely, the special case of HR- \({Q}_{L}^{U}\) where each hospital has only a lower quota but no upper quota and the variation of HR- \({Q}_{L}^{U}\) where hospitals do not have preferences over residents, which is also known as the House Allocation problem with lower and upper quotas.

We thank Robert Bredereck and Rolf Niedermeier for useful discussions.

N. Boehmer—supported by the DFG project MaMu (NI 369/19).

K. Heeger—supported by DFG Research Training Group 2434 “Facets of Complexity”.

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Authors and Affiliations

  1. Algorithmics and Computational Complexity, TU Berlin, Berlin, Germany

    Niclas Boehmer & Klaus Heeger

Authors
  1. Niclas Boehmer
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  2. Klaus Heeger
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Correspondence to Niclas Boehmer .

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Editors and Affiliations

  1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China

    Xujin Chen

  2. Shanghai University of Finance and Economics, Shanghai, China

    Nikolai Gravin

  3. Goethe University Frankfurt, Frankfurt am Main, Germany

    Martin Hoefer

  4. University of Illinois at Urbana-Champaign, Urbana, IL, USA

    Ruta Mehta

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Boehmer, N., Heeger, K. (2020). A Fine-Grained View on Stable Many-To-One Matching Problems with Lower and Upper Quotas. In: Chen, X., Gravin, N., Hoefer, M., Mehta, R. (eds) Web and Internet Economics. WINE 2020. Lecture Notes in Computer Science(), vol 12495. Springer, Cham. https://doi.org/10.1007/978-3-030-64946-3_3

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  • DOI: https://doi.org/10.1007/978-3-030-64946-3_3

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