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Heuristic Computation of Exact Treewidth

Author Hisao Tamaki

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Author Details

Hisao Tamaki
  • Department of Computer Science, Meiji University, Tokyo, Japan

Acknowledgements

I thank Holger Dell for posing the challenging bonus instances, which have kept defying my "great ideas", showing how they fail, and pointing to yet greater ideas.

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Hisao Tamaki. Heuristic Computation of Exact Treewidth. In 20th International Symposium on Experimental Algorithms (SEA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 233, pp. 17:1-17:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.SEA.2022.17

Abstract

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 The upper bound algorithm extends and simplifies the present author’s unpublished work on a heuristic use of the dynamic programming algorithm for deciding treewidth due to Bouchitté and Todinca.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 H_0 of G, the algorithm tries to construct a sequence of minors H_0, H_1, ..., H_k with tw(H_i) < tw(H_{i + 1}) for 0 ≤ i < k and hopefully tw(H_k) = 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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
Keywords
  • graph algorithm
  • treewidth
  • heuristics
  • BT dynamic programming
  • contraction
  • obstruction
  • minimal forbidden minor
  • certifying algorithms

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References

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