TY - GEN
T1 - Stable Matching with Multilayer Approval Preferences
T2 - 15th International Symposium on Algorithmic Game Theory, SAGT 2022
AU - Bentert, Matthias
AU - Boehmer, Niclas
AU - Heeger, Klaus
AU - Koana, Tomohiro
N1 - Publisher Copyright:
© 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.
PY - 2022/1/1
Y1 - 2022/1/1
N2 - We study stable matching problems where agents have multilayer preferences: There are ℓ layers each consisting of one preference relation for each agent. Recently, Chen et al. [EC ’18] studied such problems with strict preferences, establishing four multilayer adaptations of classical notions of stability. We follow up on their work by analyzing the computational complexity of stable matching problems with multilayer approval preferences. We consider eleven stability notions derived from three well-established stability notions for stable matchings with ties and the four adaptations proposed by Chen et al. For each stability notion, we show that the problem of finding a stable matching is either polynomial-time solvable or NP-hard. Furthermore, we examine the influence of the number of layers and the desired “degree of stability” on the problems’ complexity. Somewhat surprisingly, we discover that assuming approval preferences instead of strict preferences does not considerably simplify the situation (and sometimes even makes polynomial-time solvable problems NP-hard).
AB - We study stable matching problems where agents have multilayer preferences: There are ℓ layers each consisting of one preference relation for each agent. Recently, Chen et al. [EC ’18] studied such problems with strict preferences, establishing four multilayer adaptations of classical notions of stability. We follow up on their work by analyzing the computational complexity of stable matching problems with multilayer approval preferences. We consider eleven stability notions derived from three well-established stability notions for stable matchings with ties and the four adaptations proposed by Chen et al. For each stability notion, we show that the problem of finding a stable matching is either polynomial-time solvable or NP-hard. Furthermore, we examine the influence of the number of layers and the desired “degree of stability” on the problems’ complexity. Somewhat surprisingly, we discover that assuming approval preferences instead of strict preferences does not considerably simplify the situation (and sometimes even makes polynomial-time solvable problems NP-hard).
UR - http://www.scopus.com/inward/record.url?scp=85138823550&partnerID=8YFLogxK
U2 - 10.1007/978-3-031-15714-1_25
DO - 10.1007/978-3-031-15714-1_25
M3 - Conference contribution
AN - SCOPUS:85138823550
SN - 9783031157134
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 436
EP - 453
BT - Algorithmic Game Theory - 15th International Symposium, SAGT 2022, Proceedings
A2 - Kanellopoulos, Panagiotis
A2 - Kyropoulou, Maria
A2 - Voudouris, Alexandros
PB - Springer Science and Business Media Deutschland GmbH
Y2 - 12 September 2022 through 15 September 2022
ER -