Fixed-Parameter Tractable Algorithm and Polynomial Kernel for Max-Cut Above Spanning Tree

Jayakrishnan Madathil, Saket Saurabh, Meirav Zehavi

Research output: Contribution to journalArticlepeer-review

5 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(8 knO ( 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
Pages (from-to)62-100
Number of pages39
JournalTheory of Computing Systems
Volume64
Issue number1
DOIs
StatePublished - 1 Jan 2020

Keywords

  • Above guarantee parameterization
  • Fixed-parameter tractable algorithm
  • Max-Cut
  • Polynomial kernel

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Theory and Mathematics

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