On the Parameterized Complexity of Computing Balanced Partitions in Graphs

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F15%3A00237632" target="_blank" >RIV/68407700:21240/15:00237632 - isvavai.cz</a>

Výsledek na webu

<a href="http://link.springer.com/article/10.1007%2Fs00224-014-9557-5" target="_blank" >http://link.springer.com/article/10.1007%2Fs00224-014-9557-5</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00224-014-9557-5" target="_blank" >10.1007/s00224-014-9557-5</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On the Parameterized Complexity of Computing Balanced Partitions in Graphs

Popis výsledku v původním jazyce

A balanced partition is a clustering of a graph into a given number of equal-sized parts. For instance, the textsc{Bisection} problem asks to remove at most $k$ edges in order to partition the vertices into two equal-sized parts. We prove that textsc{Bisection} is FPT for the distance to constant cliquewidth if we are given the deletion set. This implies FPT algorithms for some well-studied parameters such as cluster vertex deletion number and feedback vertex set. However, we show that textsc{Bisection}does not admit polynomial-size kernels for these parameters. For the textsc{Vertex Bisection} problem, vertices need to be removed in order to obtain two equal-sized parts. We show that this problem is FPT for the number of removed vertices $k$ if the solution cuts the graph into a constant number $c$ of connected components. The latter condition is unavoidable, since we also prove that textsc{Vertex Bisection} is W[1]-hard w.r.t.~$(k,c)$. Our algorithms for finding bisections can easil

Název v anglickém jazyce

On the Parameterized Complexity of Computing Balanced Partitions in Graphs

Popis výsledku anglicky

A balanced partition is a clustering of a graph into a given number of equal-sized parts. For instance, the textsc{Bisection} problem asks to remove at most $k$ edges in order to partition the vertices into two equal-sized parts. We prove that textsc{Bisection} is FPT for the distance to constant cliquewidth if we are given the deletion set. This implies FPT algorithms for some well-studied parameters such as cluster vertex deletion number and feedback vertex set. However, we show that textsc{Bisection}does not admit polynomial-size kernels for these parameters. For the textsc{Vertex Bisection} problem, vertices need to be removed in order to obtain two equal-sized parts. We show that this problem is FPT for the number of removed vertices $k$ if the solution cuts the graph into a constant number $c$ of connected components. The latter condition is unavoidable, since we also prove that textsc{Vertex Bisection} is W[1]-hard w.r.t.~$(k,c)$. Our algorithms for finding bisections can easil

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

IN - Informatika

OECD FORD obor

—

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2015

Kód důvěrnosti údajů

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

Název periodika

Theory of Computing Systems

ISSN

1432-4350

e-ISSN

—

Svazek periodika

57

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

35

Strana od-do

1-35

Kód UT WoS článku

000358741300001

EID výsledku v databázi Scopus

2-s2.0-84937191674