Lazy Gale-Shapley for Many-to-One Matching with Partial Information

Taiki Todo, Ryoji Wada, Kentaro Yahiro, Makoto Yokoo

研究成果: Chapter in Book/Report/Conference proceedingConference contribution

抄録

In the literature of two-sided matching, each agent is assumed to have a complete preference. In practice, however, each agent initially has only partial information and needs to refine it by costly actions (interviews). For one-to-one matching with partial information, the student-proposing Lazy Gale-Shapley policy (LGS) minimizes the number of interviews when colleges have identical partial preferences. This paper extends LGS to a significantly more practical many-to-one setting, in which a college can accept multiple students up to its quota. Our extended LGS uses a student hierarchy and its performance (in terms of the required number of interviews) depends on the choice of this hierarchy. We prove that when colleges’ partial preferences satisfy a condition called compatibility, we can obtain an optimal hierarchy that minimizes the number of interviews in polynomial-time. Furthermore, we propose a heuristic method to obtain a reasonable hierarchy when compatibility fails. We experimentally confirm that compatibility is actually much weaker than being identical, i.e., when the partial preferences of each college are obtained by adding noise to an ideal true preference, our requirement is much more robust against such noise. We also experimentally confirm that our heuristic method obtains a reasonable hierarchy to reduce the number of required interviews.

本文言語英語
ホスト出版物のタイトルAlgorithmic Decision Theory - 7th International Conference, ADT 2021, Proceedings
編集者Dimitris Fotakis, David Ríos Insua
出版社Springer Science and Business Media Deutschland GmbH
ページ390-405
ページ数16
ISBN(印刷版)9783030877552
DOI
出版ステータス出版済み - 2021
イベント7th International Conference on Algorithmic Decision Theory, ADT 2021 - Toulouse, フランス
継続期間: 11 3 202111 5 2021

出版物シリーズ

名前Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
13023 LNAI
ISSN(印刷版)0302-9743
ISSN(電子版)1611-3349

会議

会議7th International Conference on Algorithmic Decision Theory, ADT 2021
国/地域フランス
CityToulouse
Period11/3/2111/5/21

All Science Journal Classification (ASJC) codes

  • 理論的コンピュータサイエンス
  • コンピュータ サイエンス(全般)

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