2022/02/15 by Hisao Tamaki, Tamaki, Hisao
Computer Science · #Advanced Graph Theory Research #Complexity and Algorithms in Graphs #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #Formal Methods in Verification
paper · pdf · doi:10.48550/arxiv.2202.07793
openalex publication_date 2022/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
We are interested in computing the treewidth \tw(G) of a given graph G. Our approach is to design heuristic algorithms for computing a sequence of improving upper bounds and a sequence of improving lower bounds, which would hopefully converge to \tw(G) from both sides. The upper bound algorithm extends and simplifies Tamaki's unpublished work on a heuristic use of the dynamic programming algorithm for deciding treewidth due to Bouchitté and Todinca. The lower bound algorithm is based on the well-known fact that, for every minor H of G, we have \tw(H) ≤ \tw(G). Starting from a greedily computed minor H0 of G, the algorithm tries to construct a sequence of minors H0, H1, … Hk with \tw(Hi) < \tw(Hi + 1) for 0 ≤ i < k and hopefully \tw(Hk) = \tw(G). We have implemented a treewidth solver based on this approach and have evaluated it on the bonus instances from the exact treewidth track of PACE 2017 algorithm implementation challenge. The results show that our approach is extremely effective in tackling instances that are hard for conventional solvers. Our solver has an additional advantage over conventional ones in that it attaches a compact certificate to the lower bound it computes.