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Documents authored by Yokoi, Yu

Document
DOI: 10.4230/LIPIcs.STACS.2022.31
Maximally Satisfying Lower Quotas in the Hospitals/Residents Problem with Ties

Authors: Hiromichi Goko, Kazuhisa Makino, Shuichi Miyazaki, and Yu Yokoi

Published in: LIPIcs, Volume 219, 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)

Abstract
Motivated by the serious problem that hospitals in rural areas suffer from a shortage of residents, we study the Hospitals/Residents model in which hospitals are associated with lower quotas and the objective is to satisfy them as much as possible. When preference lists are strict, the number of residents assigned to each hospital is the same in any stable matching because of the well-known rural hospitals theorem; thus there is no room for algorithmic interventions. However, when ties are introduced to preference lists, this will no longer apply because the number of residents may vary over stable matchings. In this paper, we formulate an optimization problem to find a stable matching with the maximum total satisfaction ratio for lower quotas. We first investigate how the total satisfaction ratio varies over choices of stable matchings in four natural scenarios and provide the exact values of these maximum gaps. Subsequently, we propose a strategy-proof approximation algorithm for our problem; in one scenario it solves the problem optimally, and in the other three scenarios, which are NP-hard, it yields a better approximation factor than that of a naive tie-breaking method. Finally, we show inapproximability results for the above-mentioned three NP-hard scenarios.
Cite as

Hiromichi Goko, Kazuhisa Makino, Shuichi Miyazaki, and Yu Yokoi. Maximally Satisfying Lower Quotas in the Hospitals/Residents Problem with Ties. In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 31:1-31:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{goko_et_al:LIPIcs.STACS.2022.31,
  author =	{Goko, Hiromichi and Makino, Kazuhisa and Miyazaki, Shuichi and Yokoi, Yu},
  title =	{{Maximally Satisfying Lower Quotas in the Hospitals/Residents Problem with Ties}},
  booktitle =	{39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)},
  pages =	{31:1--31:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-222-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{219},
  editor =	{Berenbrink, Petra and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2022.31},
  URN =		{urn:nbn:de:0030-drops-158414},
  doi =		{10.4230/LIPIcs.STACS.2022.31},
  annote =	{Keywords: Stable matching, Hospitals/Residents problem, Lower quota, NP-hardness, Approximation algorithm, Strategy-proofness}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2021.71
An Approximation Algorithm for Maximum Stable Matching with Ties and Constraints

Authors: Yu Yokoi

Published in: LIPIcs, Volume 212, 32nd International Symposium on Algorithms and Computation (ISAAC 2021)

Abstract
We present a polynomial-time 3/2-approximation algorithm for the problem of finding a maximum-cardinality stable matching in a many-to-many matching model with ties and laminar constraints on both sides. We formulate our problem using a bipartite multigraph whose vertices are called workers and firms, and edges are called contracts. Our algorithm is described as the computation of a stable matching in an auxiliary instance, in which each contract is replaced with three of its copies and all agents have strict preferences on the copied contracts. The construction of this auxiliary instance is symmetric for the two sides, which facilitates a simple symmetric analysis. We use the notion of matroid-kernel for computation in the auxiliary instance and exploit the base-orderability of laminar matroids to show the approximation ratio. In a special case in which each worker is assigned at most one contract and each firm has a strict preference, our algorithm defines a 3/2-approximation mechanism that is strategy-proof for workers.
Cite as

Yu Yokoi. An Approximation Algorithm for Maximum Stable Matching with Ties and Constraints. In 32nd International Symposium on Algorithms and Computation (ISAAC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 212, pp. 71:1-71:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{yokoi:LIPIcs.ISAAC.2021.71,
  author =	{Yokoi, Yu},
  title =	{{An Approximation Algorithm for Maximum Stable Matching with Ties and Constraints}},
  booktitle =	{32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
  pages =	{71:1--71:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-214-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{212},
  editor =	{Ahn, Hee-Kap and Sadakane, Kunihiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2021.71},
  URN =		{urn:nbn:de:0030-drops-155047},
  doi =		{10.4230/LIPIcs.ISAAC.2021.71},
  annote =	{Keywords: Stable matching, Approximation algorithm, Matroid, Strategy-proofness}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2017.67
Envy-free Matchings with Lower Quotas

Authors: Yu Yokoi

Published in: LIPIcs, Volume 92, 28th International Symposium on Algorithms and Computation (ISAAC 2017)

Abstract
While every instance of the Hospitals/Residents problem admits a stable matching, the problem with lower quotas (HR-LQ) has instances with no stable matching. For such an instance, we expect the existence of an envy-free matching, which is a relaxation of a stable matching preserving a kind of fairness property. In this paper, we investigate the existence of an envy-free matching in several settings, in which hospitals have lower quotas. We first provide an algorithm that decides whether a given HR-LQ instance has an envy-free matching or not. Then, we consider envy-freeness in the Classified Stable Matching model due to Huang (2010), i.e., each hospital has lower and upper quotas on subsets of doctors. We show that, for this model, deciding the existence of an envy-free matching is NP-hard in general, but solvable in polynomial time if quotas are paramodular.
Cite as

Yu Yokoi. Envy-free Matchings with Lower Quotas. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 67:1-67:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{yokoi:LIPIcs.ISAAC.2017.67,
  author =	{Yokoi, Yu},
  title =	{{Envy-free Matchings with Lower Quotas}},
  booktitle =	{28th International Symposium on Algorithms and Computation (ISAAC 2017)},
  pages =	{67:1--67:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-054-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{92},
  editor =	{Okamoto, Yoshio and Tokuyama, Takeshi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.67},
  URN =		{urn:nbn:de:0030-drops-82205},
  doi =		{10.4230/LIPIcs.ISAAC.2017.67},
  annote =	{Keywords: stable matchings, envy-free matchings, lower quotas, polynomial time algorithm, paramodular functions}
}
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