Exact algorithms for counting 3-colorings of graphs

Graph Coloring Problem, as one of the best known NP-complete problems, has been extensively studied by researchers in a wide range of fields, leading to many applications and theories in mathematics and computer science. In this paper, we focus on the design of exact algorithms for counting 3-colori...

Full description

Saved in:

Bibliographic Details
Published in:	Discrete Applied Mathematics Vol. 322; pp. 74 - 93
Main Authors:	Zhu, Enqiang, Wu, Pu, Shao, Zehui
Format:	Journal Article
Language:	English
Published:	Elsevier B.V 15.12.2022
Subjects:	3-Coloring Branch and reduce Dynamic programming Exact exponential-time algorithms Measure and conquer Measure and conquer Branch and reduce 3-Coloring Dynamic programming Exact exponential-time algorithms
ISSN:	0166-218X, 1872-6771
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Description
Summary:	Graph Coloring Problem, as one of the best known NP-complete problems, has been extensively studied by researchers in a wide range of fields, leading to many applications and theories in mathematics and computer science. In this paper, we focus on the design of exact algorithms for counting 3-colorings of a graph (denoted by #3-Coloring). Our approach is based on branch and reduce paradigm. We use the measure and conquer method to analyze the algorithms, in which we design two sets of measures (weights of vertices) intended for two distinct situations. In particular, we use the tree-width based technique to handle a special case by leveraging dynamic programming. As a result, we obtain an O(1.588n)-time algorithm for the #3-Coloring problem, which improves the previous O(1.6262n)-time algorithm by Fomin et al. (2007).
ISSN:	0166-218X 1872-6771
DOI:	10.1016/j.dam.2022.08.002