Degreewidth: A New Parameter for Solving Problems on Tournaments

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

Degreewidth: A New Parameter for Solving Problems on Tournaments

Original language description

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.

Czech name

—

Czech description

—

Type

D - Article in proceedings

CEP classification

—

OECD FORD branch

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

Project

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2023

Confidentiality

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

Article name in the collection

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

Number of pages

15

Pages from-to

246-260

Publisher name

Springer

Place of publication

Cham

Event location

Fribourg

Event date

Jun 28, 2023

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

001162209000018