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An Improved DSATUR‐Based Branch‐and‐Bound Algorithm for the Vertex Coloring Problem
Author(s) -
Furini Fabio,
Gabrel Virginie,
Ternier IanChristopher
Publication year - 2017
Publication title -
networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.977
H-Index - 64
eISSN - 1097-0037
pISSN - 0028-3045
DOI - 10.1002/net.21716
Subject(s) - vertex (graph theory) , upper and lower bounds , combinatorics , computation , branch and bound , mathematics , algorithm , fractional coloring , graph , computer science , graph power , line graph , mathematical analysis
Given an undirected graph, the Vertex Coloring Problem (VCP) consists of assigning a color to each vertex of the graph in such a way that two adjacent vertices do not share the same color and the total number of colors is minimized. DSATUR‐based Branch‐and‐Bound algorithm (DSATUR) is an effective exact algorithm for the VCP. One of its main drawback is that a lower bound is computed only once and it is never updated. We introduce a reduced graph which allows the computation of lower bounds at nodes of the branching tree. We compare the effectiveness of different classical VCP bounds, plus a new lower bound based on the 1 ‐to‐ 1 mapping between VCPs and Stable Set Problems. Our new DSATUR outperforms the state of the art for random VCP instances with high density, significantly increasing the size of instances solved to proven optimality. © 2016 Wiley Periodicals, Inc. NETWORKS, Vol. 69(1), 124–141 2017