Improving Vertex Cover as a Graph Parameter

Parameterized algorithms are often used to efficiently solve NP-hard problems on graphs. In this context, vertex cover is used as a powerful parameter for dealing with graph problems which are hard to solve even when parameterized by tree-width; however, the drawback of vertex cover is that bounding...

Full description

Saved in:
Bibliographic Details
Published in:Discrete Mathematics and Theoretical Computer Science Vol. 17 no.2; no. Discrete Algorithms; pp. 77 - 100
Main Author: Ganian, Robert
Format: Journal Article
Language:English
Published: Nancy DMTCS 14.09.2015
Discrete Mathematics & Theoretical Computer Science
Subjects:
[info.info-dm] computer science [cs]/discrete mathematics [cs.dm]
Analysis
Computational complexity
Computer Science
Discrete Mathematics
Graph theory
Graphs
Mathematics
Parameter estimation
parameterized complexity
twin-cover
vertex cover
United States
Twin-cover
Vertex cover
Parameterized Complexity
ISSN:1365-8050, 1462-7264, 1365-8050
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Parameterized algorithms are often used to efficiently solve NP-hard problems on graphs. In this context, vertex cover is used as a powerful parameter for dealing with graph problems which are hard to solve even when parameterized by tree-width; however, the drawback of vertex cover is that bounding it severely restricts admissible graph classes. We introduce a generalization of vertex cover called twin-cover and show that FPT algorithms exist for a wide range of difficult problems when parameterized by twin-cover. The advantage of twin-cover over vertex cover is that it imposes a lesser restriction on the graph structure and attains low values even on dense graphs. Apart from introducing the parameter itself, this article provides a number of new FPT algorithms parameterized by twin-cover with a special emphasis on solving problems which are not in FPT even when parameterized by tree-width. It also shows that MS1 model checking can be done in elementary FPT time parameterized by twin-cover and discusses the field of kernelization.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1365-8050
1462-7264
1365-8050
DOI:10.46298/dmtcs.2136