Solving Partial Dominating Set and Related Problems Using Twin-Width

Kód výsledku v IS VaVaI

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Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Solving Partial Dominating Set and Related Problems Using Twin-Width

Popis výsledku v původním jazyce

Partial vertex cover and partial dominating set are two well-investigated optimization problems. While they are $rm W[1]$-hard on general graphs, they have been shown to be fixed-parameter tractable on many sparse graph classes, including nowhere-dense classes. In this paper, we demonstrate that these problems are also fixed-parameter tractable with respect to the twin-width of a graph. Indeed, we establish a more general result: every graph property that can be expressed by a logical formula of the form phiequivexists x_1cdots exists x_k sum_{iin I} #y,psi_i(x_1,ldots,x_k,y)ge t$, where $psi_i$ is a quantifier-free formula for each $i in I$, $t$ is an arbitrary number, and $#y$ is a counting quantifier, can be evaluated in time $f(d,k)n$, where $n$ is the number of vertices and $d$ is the width of a contraction sequence that is part of the input. In addition to the aforementioned problems, this includes also connected partial dominating set and independent partial dominating set.

Název v anglickém jazyce

Solving Partial Dominating Set and Related Problems Using Twin-Width

Popis výsledku anglicky

Partial vertex cover and partial dominating set are two well-investigated optimization problems. While they are $rm W[1]$-hard on general graphs, they have been shown to be fixed-parameter tractable on many sparse graph classes, including nowhere-dense classes. In this paper, we demonstrate that these problems are also fixed-parameter tractable with respect to the twin-width of a graph. Indeed, we establish a more general result: every graph property that can be expressed by a logical formula of the form phiequivexists x_1cdots exists x_k sum_{iin I} #y,psi_i(x_1,ldots,x_k,y)ge t$, where $psi_i$ is a quantifier-free formula for each $i in I$, $t$ is an arbitrary number, and $#y$ is a counting quantifier, can be evaluated in time $f(d,k)n$, where $n$ is the number of vertices and $d$ is the width of a contraction sequence that is part of the input. In addition to the aforementioned problems, this includes also connected partial dominating set and independent partial dominating set.

Druh

D - Stať ve sborníku

CEP obor

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OECD FORD obor

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

Projekt

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Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2025

Kód důvěrnosti údajů

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

Název statě ve sborníku

50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

ISBN

9783959773881

ISSN

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e-ISSN

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Počet stran výsledku

19

Strana od-do

„13:1“-„13:19“

Název nakladatele

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

Místo vydání

Dagstuhl

Místo konání akce

Varšava

Datum konání akce

25. 8. 2025

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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