Turbocharging Treewidth Heuristics

A widely used class of algorithms for computing tree decompositions of graphs are heuristics that compute an elimination order, i.e., a permutation of the vertex set. In this paper, we propose to turbocharge these heuristics. For a target treewidth k , suppose the heuristic has already computed a partial elimination order of width at most k , but extending it by one more vertex exceeds the target width k . At this moment of regret , we solve a subproblem which is to recompute the last c positions of the partial elimination order such that it can be extended without exceeding width k . We show that this subproblem is fixed-parameter tractable when parameterized by k and c , but it is para-NP-hard and W [1]-hard when parameterized by only k or c , respectively. Our experimental evaluation of the FPT algorithm shows that we can trade a reasonable increase of the running time for the quality of the solution.