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

Taiki Todo, Ryoji Wada, Kentaro Yahiro, Makoto Yokoo

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

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.

Original languageEnglish
Title of host publicationAlgorithmic Decision Theory - 7th International Conference, ADT 2021, Proceedings
EditorsDimitris Fotakis, David Ríos Insua
PublisherSpringer Science and Business Media Deutschland GmbH
Pages390-405
Number of pages16
ISBN (Print)9783030877552
DOIs
Publication statusPublished - 2021
Event7th International Conference on Algorithmic Decision Theory, ADT 2021 - Toulouse, France
Duration: Nov 3 2021Nov 5 2021

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13023 LNAI
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference7th International Conference on Algorithmic Decision Theory, ADT 2021
Country/TerritoryFrance
CityToulouse
Period11/3/2111/5/21

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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