eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-29
30:1
30:21
10.4230/LIPIcs.FSTTCS.2021.30
article
Popular Matchings in the Hospital-Residents Problem with Two-Sided Lower Quotas
Nasre, Meghana
1
Nimbhorkar, Prajakta
2
3
Ranjan, Keshav
1
Sarkar, Ankita
4
IIT Madras, Chennai, India
Chennai Mathematical Institute, India
UMI ReLaX, Chennai, India
Dartmouth College, Hanover, NH, USA
We consider the hospital-residents problem where both hospitals and residents can have lower quotas. The input is a bipartite graph G = (ℛ∪ℋ,E), each vertex in ℛ∪ℋ has a strict preference ordering over its neighbors. The sets ℛ and ℋ denote the sets of residents and hospitals respectively. Each hospital has an upper and a lower quota denoting the maximum and minimum number of residents that can be assigned to it. Residents have upper quota equal to one, however, there may be a requirement that some residents must not be left unassigned in the output matching. We call this as the residents' lower quota.
We show that whenever the set of matchings satisfying all the lower and upper quotas is non-empty, there always exists a matching that is popular among the matchings in this set. We give a polynomial-time algorithm to compute such a matching.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol213-fsttcs2021/LIPIcs.FSTTCS.2021.30/LIPIcs.FSTTCS.2021.30.pdf
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