TY - GEN

T1 - Parameterized complexity of critical node cuts

AU - Hermelin, Danny

AU - Kaspi, Moshe

AU - Komusiewicz, Christian

AU - Navon, Barak

N1 - Publisher Copyright: © Danny Hermelin, Moshe Kaspi, Christian Komusiewicz, and Barak Navon;.

PY - 2015/11/1

Y1 - 2015/11/1

N2 - We consider the following graph cut problem called Critical Node Cut (CNC): Given a graph G on n vertices, and two positive integers κ and x, determine whether G has a set of κ vertices whose removal leaves G with at most x connected pairs of vertices. We analyze this problem in the framework of parameterized complexity. That is, we are interested in whether or not this problem is solvable in f(κ) · nO(1) time (i.e., whether or not it is fixed-parameter tractable), for various natural parameters κ. We consider four such parameters: The size κ of the required cut. The upper bound x on the number of remaining connected pairs. The lower bound y on the number of connected pairs to be removed. The treewidth w of G. We determine whether or not CNC is fixed-parameter tractable for each of these parameters. We determine this also for all possible aggregations of these four parameters, apart from w + κ. Moreover, we also determine whether or not CNC admits a polynomial kernel for all these parameterizations. That is, whether or not there is an algorithm that reduces each instance of CNC in polynomial time to an equivalent instance of size κO(1), where κ is the given parameter.

AB - We consider the following graph cut problem called Critical Node Cut (CNC): Given a graph G on n vertices, and two positive integers κ and x, determine whether G has a set of κ vertices whose removal leaves G with at most x connected pairs of vertices. We analyze this problem in the framework of parameterized complexity. That is, we are interested in whether or not this problem is solvable in f(κ) · nO(1) time (i.e., whether or not it is fixed-parameter tractable), for various natural parameters κ. We consider four such parameters: The size κ of the required cut. The upper bound x on the number of remaining connected pairs. The lower bound y on the number of connected pairs to be removed. The treewidth w of G. We determine whether or not CNC is fixed-parameter tractable for each of these parameters. We determine this also for all possible aggregations of these four parameters, apart from w + κ. Moreover, we also determine whether or not CNC admits a polynomial kernel for all these parameterizations. That is, whether or not there is an algorithm that reduces each instance of CNC in polynomial time to an equivalent instance of size κO(1), where κ is the given parameter.

KW - Graph cut problem

KW - NP-hard problem

KW - Treewidth

UR - http://www.scopus.com/inward/record.url?scp=84958244728&partnerID=8YFLogxK

U2 - https://doi.org/10.4230/LIPIcs.IPEC.2015.343

DO - https://doi.org/10.4230/LIPIcs.IPEC.2015.343

M3 - Conference contribution

T3 - Leibniz International Proceedings in Informatics, LIPIcs

SP - 343

EP - 354

BT - 10th International Symposium on Parameterized and Exact Computation, IPEC 2015

A2 - Husfeldt, Thore

A2 - Kanj, Iyad

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

T2 - 10th International Symposium on Parameterized and Exact Computation, IPEC 2015

Y2 - 16 September 2015 through 18 September 2015

ER -