On the Parameterized Complexity of Finding Separators with Non-Hereditary Properties

Heggernes, Pinar and van't Hof, Pim and Marx, Daniel and Misra, Neeldhara and Villanger, Yngve (2015) On the Parameterized Complexity of Finding Separators with Non-Hereditary Properties. In: ALGORITHMICA, 72 (3). pp. 687-713.

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Abstract

We study the problem of finding small s-t separators that induce graphs having certain properties. It is known that finding a minimum clique s-t separator is polynomial-time solvable (Tarjan in Discrete Math. 55:221-232, 1985), while for example the problems of finding a minimum s-t separator that induces a connected graph or forms an independent set are fixed-parameter tractable when parameterized by the size of the separator (Marx et al. in ACM Trans. Algorithms 9(4): 30, 2013). Motivated by these results, we study properties that generalize cliques, independent sets, and connected graphs, and determine the complexity of finding separators satisfying these properties. We investigate these problems also on bounded-degree graphs. Our results are as follows: Finding a minimum c-connected s-t separator is FPT for c=2 and W1]-hard for any ca parts per thousand yen3. Finding a minimum s-t separator with diameter at most d is W1]-hard for any da parts per thousand yen2. Finding a minimum r-regular s-t separator is W1]-hard for any ra parts per thousand yen1. For any decidable graph property, finding a minimum s-t separator with this property is FPT parameterized jointly by the size of the separator and the maximum degree. Finding a connected s-t separator of minimum size does not have a polynomial kernel, even when restricted to graphs of maximum degree at most 3, unless .

Item Type:	Journal Article
Publication:	ALGORITHMICA
Publisher:	SPRINGER
Additional Information:	Copy right for this article belongs to the SPRINGER, 233 SPRING ST, NEW YORK, NY 10013 USA
Keywords:	Vertex separators; Non-hereditary properties; Parameterized complexity; FPT algorithms
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	06 Jul 2015 06:47
Last Modified:	06 Jul 2015 06:47
URI:	http://eprints.iisc.ac.in/id/eprint/51805

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