A local search algorithm for branchwidth

Abstract

As many problems can be solved in polynomial time on graphs of bounded branchwidth, there is a need for efficient and practical algorithms that find branch decompositions of small width of given graphs. In this paper, we give the first local search algorithm for this problem. Using non-trivial combinatorial properties of the neighbourhood space, significant reductions in the search space can be obtained. The fitness function can be easily tuned to express the expected cost in the dynamic programming step for specific problems. The algorithm is tested on a number of planar and non-planar graphs. For all tested planar graphs the algorithm found an optimal branch decomposition. For most non-planar graphs, we obtained branch decompositions of width equal to or smaller than the treewidth. Our experiments indicate that local search is a very suitable technique for finding branch decompositions of small width. © 2011 Springer-Verlag Berlin Heidelberg.