Parameterized complexity of stable roommates with ties and incomplete lists through the lens of graph parameters

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F19%3A00337770" target="_blank" >RIV/68407700:21240/19:00337770 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.4230/LIPIcs.ISAAC.2019.44" target="_blank" >http://dx.doi.org/10.4230/LIPIcs.ISAAC.2019.44</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4230/LIPIcs.ISAAC.2019.44" target="_blank" >10.4230/LIPIcs.ISAAC.2019.44</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Parameterized complexity of stable roommates with ties and incomplete lists through the lens of graph parameters

Popis výsledku v původním jazyce

We continue and extend previous work on the parameterized complexity analysis of the NP-hard Stable Roommates with Ties and Incomplete Lists problem, thereby strengthening earlier results both on the side of parameterized hardness as well as on the side of fixed-parameter tractability. Other than for its famous sister problem Stable Marriage which focuses on a bipartite scenario, Stable Roommates with Incomplete Lists allows for arbitrary acceptability graphs whose edges specify the possible matchings of each two agents (agents are represented by graph vertices). Herein, incomplete lists and ties reflect the fact that in realistic application scenarios the agents cannot bring all other agents into a linear order. Among our main contributions is to show that it is W[1]-hard to compute a maximum-cardinality stable matching for acceptability graphs of bounded treedepth, bounded tree-cut width, and bounded feedback vertex number (these are each time the respective parameters). However, if we `only' ask for perfect stable matchings or the mere existence of a stable matching, then we obtain fixed-parameter tractability with respect to tree-cut width but not with respect to treedepth. On the positive side, we also provide fixed-parameter tractability results for the parameter feedback edge set number.

Název v anglickém jazyce

Parameterized complexity of stable roommates with ties and incomplete lists through the lens of graph parameters

Popis výsledku anglicky

We continue and extend previous work on the parameterized complexity analysis of the NP-hard Stable Roommates with Ties and Incomplete Lists problem, thereby strengthening earlier results both on the side of parameterized hardness as well as on the side of fixed-parameter tractability. Other than for its famous sister problem Stable Marriage which focuses on a bipartite scenario, Stable Roommates with Incomplete Lists allows for arbitrary acceptability graphs whose edges specify the possible matchings of each two agents (agents are represented by graph vertices). Herein, incomplete lists and ties reflect the fact that in realistic application scenarios the agents cannot bring all other agents into a linear order. Among our main contributions is to show that it is W[1]-hard to compute a maximum-cardinality stable matching for acceptability graphs of bounded treedepth, bounded tree-cut width, and bounded feedback vertex number (these are each time the respective parameters). However, if we `only' ask for perfect stable matchings or the mere existence of a stable matching, then we obtain fixed-parameter tractability with respect to tree-cut width but not with respect to treedepth. On the positive side, we also provide fixed-parameter tractability results for the parameter feedback edge set number.

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

2019

Kód důvěrnosti údajů

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

Název statě ve sborníku

30th International Symposium on Algorithms and Computation (ISAAC 2019)

ISBN

978-3-95977-130-6

ISSN

—

e-ISSN

1868-8969

Počet stran výsledku

14

Strana od-do

"44:1"-"44:14"

Název nakladatele

Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik

Místo vydání

Dagstuhl

Místo konání akce

Shanghai

Datum konání akce

9. 12. 2019

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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