Max-cut above spanning tree is fixed-parameter tractable

Jayakrishnan Madathil, Saket Saurabh, Meirav Zehavi

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

4 Scopus citations

Abstract

Every connected graph on n vertices has a cut of size at least n − 1. We call this bound the ‘spanning tree bound’. In the Max-Cut Above Spanning Tree (Max-Cut-AST) problem, we are given a connected n-vertex graph G and a non-negative integer k, and the task is to decide whether G has a cut of size at least n − 1 + k. We show that Max-Cut-AST admits an algorithm that runs in time O(8knO(1), and hence it is fixed parameter tractable with respect to k. Furthermore, we show that Max-Cut-AST has a polynomial kernel of size O(k5).

Original languageEnglish
Title of host publicationComputer Science - Theory and Applications - 13th International Computer Science Symposium in Russia, CSR 2018, Proceedings
EditorsVladimir V. Podolskii, Fedor V. Fomin
PublisherSpringer Verlag
Pages244-256
Number of pages13
ISBN (Print)9783319905297
DOIs
StatePublished - 1 Jan 2018
Event13th International Computer Science Symposium in Russia, CSR 2018 - Moscow, Russian Federation
Duration: 6 Jun 201810 Jun 2018

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10846 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference13th International Computer Science Symposium in Russia, CSR 2018
Country/TerritoryRussian Federation
CityMoscow
Period6/06/1810/06/18

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science

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