Parameterized complexity of critical node cuts

Danny Hermelin, Moshe Kaspi, Christian Komusiewicz, Barak Navon

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


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.

Original languageAmerican English
Title of host publication10th International Symposium on Parameterized and Exact Computation, IPEC 2015
EditorsThore Husfeldt, Iyad Kanj
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Number of pages12
ISBN (Electronic)9783939897927
StatePublished - 1 Nov 2015
Event10th International Symposium on Parameterized and Exact Computation, IPEC 2015 - Patras, Greece
Duration: 16 Sep 201518 Sep 2015

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs


Conference10th International Symposium on Parameterized and Exact Computation, IPEC 2015


  • Graph cut problem
  • NP-hard problem
  • Treewidth

All Science Journal Classification (ASJC) codes

  • Software


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