TY - GEN
T1 - Lazy Gale-Shapley for Many-to-One Matching with Partial Information
AU - Todo, Taiki
AU - Wada, Ryoji
AU - Yahiro, Kentaro
AU - Yokoo, Makoto
N1 - Publisher Copyright:
© 2021, Springer Nature Switzerland AG.
PY - 2021
Y1 - 2021
N2 - 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.
AB - 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.
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U2 - 10.1007/978-3-030-87756-9_25
DO - 10.1007/978-3-030-87756-9_25
M3 - Conference contribution
AN - SCOPUS:85119006806
SN - 9783030877552
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 390
EP - 405
BT - Algorithmic Decision Theory - 7th International Conference, ADT 2021, Proceedings
A2 - Fotakis, Dimitris
A2 - Ríos Insua, David
PB - Springer Science and Business Media Deutschland GmbH
T2 - 7th International Conference on Algorithmic Decision Theory, ADT 2021
Y2 - 3 November 2021 through 5 November 2021
ER -