Computing Twin-Width Parameterized by the Feedback Edge Number

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F24%3A00135638" target="_blank" >RIV/00216224:14330/24:00135638 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.4230/LIPIcs.STACS.2024.7" target="_blank" >http://dx.doi.org/10.4230/LIPIcs.STACS.2024.7</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4230/LIPIcs.STACS.2024.7" target="_blank" >10.4230/LIPIcs.STACS.2024.7</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Computing Twin-Width Parameterized by the Feedback Edge Number

Popis výsledku v původním jazyce

The problem of whether and how one can compute the twin-width of a graph - along with an accompanying contraction sequence - lies at the forefront of the area of algorithmic model theory. While significant effort has been aimed at obtaining a fixed-parameter approximation for the problem when parameterized by twin-width, here we approach the question from a different perspective and consider whether one can obtain (near-)optimal contraction sequences under a larger parameterization, notably the feedback edge number k. As our main contributions, under this parameterization we obtain (1) a linear bikernel for the problem of either computing a 2-contraction sequence or determining that none exists and (2) an approximate fixed-parameter algorithm which computes an ????-contraction sequence (for an arbitrary specified ????) or determines that the twin-width of the input graph is at least ????. These algorithmic results rely on newly obtained insights into the structure of optimal contraction sequences, and as a byproduct of these we also slightly tighten the bound on the twin-width of graphs with small feedback edge number.

Název v anglickém jazyce

Computing Twin-Width Parameterized by the Feedback Edge Number

Popis výsledku anglicky

The problem of whether and how one can compute the twin-width of a graph - along with an accompanying contraction sequence - lies at the forefront of the area of algorithmic model theory. While significant effort has been aimed at obtaining a fixed-parameter approximation for the problem when parameterized by twin-width, here we approach the question from a different perspective and consider whether one can obtain (near-)optimal contraction sequences under a larger parameterization, notably the feedback edge number k. As our main contributions, under this parameterization we obtain (1) a linear bikernel for the problem of either computing a 2-contraction sequence or determining that none exists and (2) an approximate fixed-parameter algorithm which computes an ????-contraction sequence (for an arbitrary specified ????) or determines that the twin-width of the input graph is at least ????. These algorithmic results rely on newly obtained insights into the structure of optimal contraction sequences, and as a byproduct of these we also slightly tighten the bound on the twin-width of graphs with small feedback edge 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

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název statě ve sborníku

41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)

ISBN

9783959773119

ISSN

1868-8969

e-ISSN

—

Počet stran výsledku

19

Strana od-do

„7:1“-„7:19“

Název nakladatele

Schloss Dagstuhl -- Leibniz-Zentrum f{"u}r Informatik

Místo vydání

Dagstuhl

Místo konání akce

Clermont-Ferrand

Datum konání akce

1. 1. 2024

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

001300393400007