Computer Science > Data Structures and Algorithms
[Submitted on 18 Jun 2021 (v1), last revised 19 May 2022 (this version, v5)]
Title:Envy-freeness and Relaxed Stability for Lower-Quotas : A Parameterized Perspective
View PDFAbstract:We consider the problem of assigning agents to resources under the two-sided preference list model where resources specify an upper-quota and a lower-quota, that is, respectively the maximum and minimum number of agents that can be assigned to it. Different notions of optimality including envy-freeness and relaxed stability are investigated for this setting and the goal is to compute a largest optimal matching. Krishnaa et al. [SAGT 2020] show that in this setting, the problem of computing a maximum size envy-free matching (MAXEFM) or a maximum size relaxed stable matching (MAXRSM) is not approximable within a certain constant factor unless P = NP. This work is the first investigation of parameterized complexity of MAXEFM and MAXRSM. We show that MAXEFM is W [1]-hard and MAXRSM is para-NP-hard when parameterized on several natural parameters derived from the instance. We present kernelization results and FPT algorithms for both problems parameterized on other relevant parameters.
Submission history
From: Girija Limaye [view email][v1] Fri, 18 Jun 2021 04:55:04 UTC (32 KB)
[v2] Fri, 27 Aug 2021 05:26:53 UTC (32 KB)
[v3] Wed, 13 Oct 2021 05:12:01 UTC (37 KB)
[v4] Wed, 6 Apr 2022 05:34:21 UTC (29 KB)
[v5] Thu, 19 May 2022 07:53:04 UTC (32 KB)
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