Parallel search-and-learn techniques and graph coloring

摘要

The paper describes a parallel algorithm for graph coloring. The algorithm is based on a search-and-learn technique for combinatorial oprimization, where multiple heuristics are used to search nearly disjoint subspaces of the combinatorial search space, and the resulting solutions are analyzed for good decisions. A decision takes the form `color nodes i and j using the same color'. If a majority of the heuristics concur on coloring two nodes with the same color, the two nodes are merged into a supernode. Supernodes of more than two nodes can similarly be identified. The given graph can be collapsed into a smaller graph, the node set of which consists of supernodes. It is shown that an optimal coloring of the collapsed graph can be used to construct an optimal coloring of the original graph. Parallelism in the search-and-learn technique is prevalent in the multiple heuristic search phase, and it is easy to exploit using a multiprocessor or a multicomputer environment. In the implementation, a network of Sun workstations is used for parallelization. Experimental results are described for a number of large benchmark examples. The results show that the technique can deliver superlinear speedup and superlinear quality for large and difficult examples of node coloring.