Chen, J. and Roy, S. orcid.org/0000-0003-3633-542X (2022) Multi-Dimensional Stable Roommates in 2-Dimensional Euclidean Space. In: Leibniz International Proceedings in Informatics (LIPIcs). 30th Annual European Symposium on Algorithms (ESA 2022), 05-07 Sep 2022, Potsdam, Germany. Schloss Dagstuhl - Leibniz-Zentrum für Informatik , 36:1-36:16.
Abstract
We investigate the Euclidean d-Dimensional Stable Roommates problem, which asks whether a given set V of d n points from the 2-dimensional Euclidean space can be partitioned into n disjoint (unordered) subsets Π = {V1, , Vn} with |Vi| = d for each Vi ϵ Π such that Π is stable. Here, stability means that no point subset W ⊆ V is blocking Π, and W is said to be blocking Πif |W| = d such that Σ w ϵW δ(w,w) < Σ vϵΠ(w) δ(w, v) holds for each point w ϵ W, where Π (w) denotes the subset Vi ϵ Π which contains w and δ(a, b) denotes the Euclidean distance between points a and b. Complementing the existing known polynomial-time result for d = 2, we show that such polynomial-time algorithms cannot exist for any fixed number d ≥ 3 unless P=NP. Our result for d = 3 answers a decade-long open question in the theory of Stable Matching and Hedonic Games [18, 1, 10, 26, 21].
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © Jiehua Chen and Sanjukta Roy; licensed under Creative Commons License CC-BY 4.0 30th Annual European Symposium on Algorithms (ESA 2022). |
Keywords: | stable matchings; multidimensional stable roommates; Euclidean preferences; coalition formation games; stable cores; NP-hardness |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 14 Feb 2024 12:41 |
Last Modified: | 14 Feb 2024 12:41 |
Status: | Published |
Publisher: | Schloss Dagstuhl - Leibniz-Zentrum für Informatik |
Identification Number: | 10.4230/LIPIcs.ESA.2022.36 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:209179 |