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

Jayakrishnan Madathil; Saket Saurabh; Meirav Zehavi

doi:10.1007/s00224-018-09909-5

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

Jayakrishnan Madathil, Saket Saurabh, Meirav Zehavi

Department of Computer Science

Research output: Contribution to journal › Article › peer-review

2 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 ^kn^O ⁽ 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 language	English
Pages (from-to)	62-100
Number of pages	39
Journal	Theory of Computing Systems
Volume	64
Issue number	1
DOIs	https://doi.org/10.1007/s00224-018-09909-5
State	Published - 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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10.1007/s00224-018-09909-5

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title = "Fixed-Parameter Tractable Algorithm and Polynomial Kernel for Max-Cut Above Spanning Tree",

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).",

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AU - Saurabh, Saket

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AB - 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).

KW - Above guarantee parameterization

KW - Fixed-parameter tractable algorithm

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

Abstract

Keywords

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