On the parameterized complexity of computing graph bisections

René Van Bevern, Andreas Emil Feldmann, Manuel Sorge, Ondřej Suchý

Результат исследования: Публикации в книгах, отчётах, сборниках, трудах конференцийстатья в сборнике материалов конференциинаучнаярецензирование

7 Цитирования (Scopus)

Аннотация

The Bisection problem asks for a partition of the vertices of a graph into two equally sized sets, while minimizing the cut size. This is the number of edges connecting the two vertex sets. Bisection has been thoroughly studied in the past. However, only few results have been published that consider the parameterized complexity of this problem. We show that Bisection is FPT w.r.t. the minimum cut size if there is an optimum bisection that cuts into a given constant number of connected components. Our algorithm applies to the more general Balanced Biseparator problem where vertices need to be removed instead of edges. We prove that this problem is W[1]-hard w.r.t. the minimum cut size and the number of cut out components. For Bisection we further show that no polynomial-size kernels exist for the cut size parameter. In fact, we show this for all parameters that are polynomial in the input size and that do not increase when taking disjoint unions of graphs. We prove fixed-parameter tractability for the distance to constant cliquewidth if we are given the deletion set. This implies fixed-parameter algorithms for some well-studied parameters such as cluster vertex deletion number and feedback vertex set.

Язык оригиналаанглийский
Название основной публикацииGraph-Theoretic Concepts in Computer Science - 39th International Workshop, WG 2013, Revised Papers
ИздательSpringer-Verlag GmbH and Co. KG
Страницы76-87
Число страниц12
ISBN (печатное издание)9783642450426
DOI
СостояниеОпубликовано - 1 янв 2013
Опубликовано для внешнего пользованияДа
Событие39th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2013 - Lubeck, Германия
Продолжительность: 19 июн 201321 июн 2013

Серия публикаций

НазваниеLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Том8165 LNCS
ISSN (печатное издание)0302-9743
ISSN (электронное издание)1611-3349

Конференция

Конференция39th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2013
СтранаГермания
ГородLubeck
Период19.06.201321.06.2013

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