(K, n − k)-max-cut: An o(2p)-time algorithm and a polynomial kernel

Saket Saurabh, Meirav Zehavi

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

7 Scopus citations


Max-Cut is a well-known classical NP-hard problem. This problem asks whether the vertex-set of a given graph G = (V,E) can be partitioned into two disjoint subsets, A and B, such that there exist at least p edges with one endpoint in A and the other endpoint in B. It is well known that if p ≤ |E|/2, the answer is necessarily positive. A widelystudied variant of particular interest to parameterized complexity, called (k, n − k)-Max-Cut, restricts the size of the subset A to be exactly k. For the (k, n − k)-Max-Cut problem, we obtain an O (2p)-time algorithm, improving upon the previous best O (4p+o(p))-time algorithm, as well as the first polynomial kernel. Our algorithm relies on a delicate combination of methods and notions, including independent sets, depthsearch trees, bounded search trees, dynamic programming and treewidth, while our kernel relies on examination of the closed neighborhood of the neighborhood of a certain independent set of the graph G.

Original languageEnglish
Title of host publicationLATIN 2016
Subtitle of host publicationTheoretical Informatics - 12th Latin American Symposium, Proceedings
EditorsGonzalo Navarro, Evangelos Kranakis, Edgar Chávez
PublisherSpringer Verlag
Number of pages14
ISBN (Print)9783662495285
StatePublished - 1 Jan 2016
Externally publishedYes
Event12th Latin American Symposium on Theoretical Informatics, LATIN 2016 - Ensenada, Mexico
Duration: 11 Apr 201615 Apr 2016

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference12th Latin American Symposium on Theoretical Informatics, LATIN 2016

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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