Enhancing PC Cluster-Based Parallel Branch-and-Bound Algorithms for the Graph Coloring Problem

Satoshi TAOKA  Daisuke TAKAFUJI  Toshimasa WATANABE  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E91-A   No.4   pp.1140-1149
Publication Date: 2008/04/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e91-a.4.1140
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Selected Papers from the 20th Workshop on Circuits and Systems in Karuizawa)
parallel branch-and-bound algorithms,  combinatorial optimization problems,  MPI,  optimum solutions,  

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A branch-and-bound algorithm (BB for short) is the most general technique to deal with various combinatorial optimization problems. Even if it is used, computation time is likely to increase exponentially. So we consider its parallelization to reduce it. It has been reported that the computation time of a parallel BB heavily depends upon node-variable selection strategies. And, in case of a parallel BB, it is also necessary to prevent increase in communication time. So, it is important to pay attention to how many and what kind of nodes are to be transferred (called sending-node selection strategy). In this paper, for the graph coloring problem, we propose some sending-node selection strategies for a parallel BB algorithm by adopting MPI for parallelization and experimentally evaluate how these strategies affect computation time of a parallel BB on a PC cluster network.