TY - GEN
T1 - A Fine-Grained View on Stable Many-To-One Matching Problems with Lower and Upper Quotas
AU - Boehmer, Niclas
AU - Heeger, Klaus
N1 - Publisher Copyright:
© 2020, Springer Nature Switzerland AG.
PY - 2020/1/1
Y1 - 2020/1/1
N2 - In the Hospital Residents problem with lower and upper quotas (HR- QLU), the goal is to find a stable matching of residents to hospitals where the number of residents matched to a hospital is either between its lower and upper quota or zero [Biró et al., TCS 2010]. We analyze this problem from a parameterized perspective using several natural parameters such as the number of hospitals and the number of residents. Moreover, we present a polynomial-time algorithm that finds a stable matching if it exists on instances with maximum lower quota two. Alongside HR- QLU, we also consider two closely related models of independent interest, namely, the special case of HR- QLU where each hospital has only a lower quota but no upper quota and the variation of HR- QLU where hospitals do not have preferences over residents, which is also known as the House Allocation problem with lower and upper quotas.
AB - In the Hospital Residents problem with lower and upper quotas (HR- QLU), the goal is to find a stable matching of residents to hospitals where the number of residents matched to a hospital is either between its lower and upper quota or zero [Biró et al., TCS 2010]. We analyze this problem from a parameterized perspective using several natural parameters such as the number of hospitals and the number of residents. Moreover, we present a polynomial-time algorithm that finds a stable matching if it exists on instances with maximum lower quota two. Alongside HR- QLU, we also consider two closely related models of independent interest, namely, the special case of HR- QLU where each hospital has only a lower quota but no upper quota and the variation of HR- QLU where hospitals do not have preferences over residents, which is also known as the House Allocation problem with lower and upper quotas.
UR - http://www.scopus.com/inward/record.url?scp=85097906780&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-64946-3_3
DO - 10.1007/978-3-030-64946-3_3
M3 - Conference contribution
AN - SCOPUS:85097906780
SN - 9783030649456
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 31
EP - 44
BT - Web and Internet Economics - 16th International Conference, WINE 2020, Proceedings
A2 - Chen, Xujin
A2 - Gravin, Nikolai
A2 - Hoefer, Martin
A2 - Mehta, Ruta
PB - Springer Science and Business Media Deutschland GmbH
T2 - 16th International Conference on Web and Internet Economics, WINE 2020
Y2 - 7 December 2020 through 11 December 2020
ER -