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DOI: 10.4230/LIPIcs.ESA.2022.36
URN: urn:nbn:de:0030-drops-169741
URL: https://drops.dagstuhl.de/opus/volltexte/2022/16974/
Chen, Jiehua ; Roy, Sanjukta
Multi-Dimensional Stable Roommates in 2-Dimensional Euclidean Space
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Abstract
We investigate the Euclidean š½-Dimensional Stable Roommates problem, which asks whether a given set V of š½ā n points from the 2-dimensional Euclidean space can be partitioned into n disjoint (unordered) subsets Ī = {Vā,ā¦,V_{n}} with |V_i| = š½ for each V_i ā Ī such that Ī is {stable}. Here, {stability} means that no point subset W ā V is blocking Ī , and W is said to be {blocking} Ī if |W| = š½ such that ā_{w' ā W}Ī“(w,w') < ā_{v ā Ī (w)}Ī“(w,v) holds for each point w ā W, where Ī (w) denotes the subset V_i ā Ī which contains w and Ī“(a,b) denotes the Euclidean distance between points a and b. Complementing the existing known polynomial-time result for š½ = 2, we show that such polynomial-time algorithms cannot exist for any fixed number š½ ā„ 3 unless P=NP. Our result for š½ = 3 answers a decade-long open question in the theory of Stable Matching and Hedonic Games [Iwama et al., 2007; Arkin et al., 2009; Vladimir G. Deineko and Gerhard J. Woeginger, 2013; Vladimir G. Deineko and Gerhard J. Woeginger, 2013; David F. Manlove, 2013].
BibTeX - Entry
@InProceedings{chen_et_al:LIPIcs.ESA.2022.36,
author = {Chen, Jiehua and Roy, Sanjukta},
title = {{Multi-Dimensional Stable Roommates in 2-Dimensional Euclidean Space}},
booktitle = {30th Annual European Symposium on Algorithms (ESA 2022)},
pages = {36:1--36:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-247-1},
ISSN = {1868-8969},
year = {2022},
volume = {244},
editor = {Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva and Herman, Grzegorz},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2022/16974},
URN = {urn:nbn:de:0030-drops-169741},
doi = {10.4230/LIPIcs.ESA.2022.36},
annote = {Keywords: stable matchings, multidimensional stable roommates, Euclidean preferences, coalition formation games, stable cores, NP-hardness}
}
| Keywords: | stable matchings, multidimensional stable roommates, Euclidean preferences, coalition formation games, stable cores, NP-hardness | |
| Seminar: | 30th Annual European Symposium on Algorithms (ESA 2022) | |
| Issue date: | 2022 | |
| Date of publication: | 01.09.2022 |
