Degreewidth: A New Parameter for Solving Problems on Tournaments

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F23%3A00368909" target="_blank" >RIV/68407700:21240/23:00368909 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/978-3-031-43380-1_18" target="_blank" >https://doi.org/10.1007/978-3-031-43380-1_18</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-031-43380-1_18" target="_blank" >10.1007/978-3-031-43380-1_18</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Degreewidth: A New Parameter for Solving Problems on Tournaments

Popis výsledku v původním jazyce

In the paper, we define a new parameter for tournaments called degreewidth which can be seen as a measure of how far is the tournament from being acyclic. The degreewidth of a tournament T denoted by is the minimum value k for which we can find an ordering of the vertices of T such that every vertex is incident to at most k backward arcs (i.e. an arc such that ). Thus, a tournament is acyclic if and only if its degreewidth is zero. Additionally, the class of sparse tournaments defined by Bessy et al. [ESA 2017] is exactly the class of tournaments with degreewidth one. We study computational complexity of finding degreewidth. We show it is NP-hard and complement this result with a 3-approximation algorithm. We provide a -time algorithm to decide if a tournament is sparse, where n is its number of vertices. Finally, we study classical graph problems DOMINATING SET and FEEDBACK VERTEX SET parameterized by degreewidth. We show the former is fixed-parameter tractable whereas the latter is NP-hard even on sparse tournaments. Additionally, we show polynomial time algorithm for FEEDBACK ARC SET on sparse tournaments.

Název v anglickém jazyce

Degreewidth: A New Parameter for Solving Problems on Tournaments

Popis výsledku anglicky

In the paper, we define a new parameter for tournaments called degreewidth which can be seen as a measure of how far is the tournament from being acyclic. The degreewidth of a tournament T denoted by is the minimum value k for which we can find an ordering of the vertices of T such that every vertex is incident to at most k backward arcs (i.e. an arc such that ). Thus, a tournament is acyclic if and only if its degreewidth is zero. Additionally, the class of sparse tournaments defined by Bessy et al. [ESA 2017] is exactly the class of tournaments with degreewidth one. We study computational complexity of finding degreewidth. We show it is NP-hard and complement this result with a 3-approximation algorithm. We provide a -time algorithm to decide if a tournament is sparse, where n is its number of vertices. Finally, we study classical graph problems DOMINATING SET and FEEDBACK VERTEX SET parameterized by degreewidth. We show the former is fixed-parameter tractable whereas the latter is NP-hard even on sparse tournaments. Additionally, we show polynomial time algorithm for FEEDBACK ARC SET on sparse tournaments.

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

2023

Kód důvěrnosti údajů

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

Název statě ve sborníku

Proceedings of the 49th International Workshop on Graph-Theoretic Concepts in Computer Science

ISBN

978-3-031-43379-5

ISSN

0302-9743

e-ISSN

1611-3349

Počet stran výsledku

15

Strana od-do

246-260

Název nakladatele

Springer

Místo vydání

Cham

Místo konání akce

Fribourg

Datum konání akce

28. 6. 2023

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

001162209000018