Search Space Reduction through Commitments in Pathwidth Computation: An Experimental Study

In designing an XP algorithm for pathwidth of digraphs, Tamaki introduced the notion of commitments and used them to reduce the search space with naively O(n!) states to one with n O(k) states, where n is the number of vertices and k is the pathwidth of the given digraph. The goal of the current work is to evaluate the potential of commitments in heuristic algorithms for the pathwidth of undirected graphs that are aimed to work well in practice even for graphs with large pathwidth. We classify commitments by a simple parameter called depth. Through experiments performed on TreewidthLIB instances, we show that depth-1 commitments are extremely effective in reducing the search space and lead to a practical algorithm capable of computing the pathwidth of many instances for which the exact pathwidth was not previously known. On the other hand, we find that the additional search space reduction enabled by depth-d commitments with 2 ≤ d ≤ 10 is limited and that there is little hope for effective heuristics based on commitments with such depth.