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

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 languageAmerican English
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

Conference

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

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science

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