Multi-Dimensional Stable Roommates in 2-Dimensional Euclidean Space

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F22%3A00359296" target="_blank" >RIV/68407700:21240/22:00359296 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.4230/LIPIcs.ESA.2022.36" target="_blank" >https://doi.org/10.4230/LIPIcs.ESA.2022.36</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4230/LIPIcs.ESA.2022.36" target="_blank" >10.4230/LIPIcs.ESA.2022.36</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Multi-Dimensional Stable Roommates in 2-Dimensional Euclidean Space

Popis výsledku v původním jazyce

We investigate the Euclidean ????-Dimensional Stable Roommates problem, which asks whether a given set V of ????⋅ n points from the 2-dimensional Euclidean space can be partitioned into n disjoint (unordered) subsets Π = {V₁,...,V_{n}} with |V_i| = ???? for each V_i element 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} Π if |W| = ???? such that ∑_{w' element W}δ(w,w') < ∑_{v element Π(w)}δ(w,v) holds for each point w element W, where Π(w) denotes the subset V_i element 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 ???? = 2, we show that such polynomial-time algorithms cannot exist for any fixed number ???? >= 3 unless P=NP. Our result for ???? = 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].

Název v anglickém jazyce

Multi-Dimensional Stable Roommates in 2-Dimensional Euclidean Space

Popis výsledku anglicky

We investigate the Euclidean ????-Dimensional Stable Roommates problem, which asks whether a given set V of ????⋅ n points from the 2-dimensional Euclidean space can be partitioned into n disjoint (unordered) subsets Π = {V₁,...,V_{n}} with |V_i| = ???? for each V_i element 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} Π if |W| = ???? such that ∑_{w' element W}δ(w,w') < ∑_{v element Π(w)}δ(w,v) holds for each point w element W, where Π(w) denotes the subset V_i element 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 ???? = 2, we show that such polynomial-time algorithms cannot exist for any fixed number ???? >= 3 unless P=NP. Our result for ???? = 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].

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

30th Annual European Symposium on Algorithms (ESA 2022)

ISBN

978-3-95977-247-1

ISSN

—

e-ISSN

1868-8969

Počet stran výsledku

16

Strana od-do

"36:1"-"36:16"

Název nakladatele

Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik

Místo vydání

Dagstuhl

Místo konání akce

Postdam

Datum konání akce

5. 9. 2022

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

—