论文信息 - On Tamaki's Algorithm to Compute Treewidths

On Tamaki's Algorithm to Compute Treewidths

We revisit the exact algorithm to compute the treewidth of a graph of Tamaki and present it in a way that facilitates improvements. The so-called I-blocks and O-blocks enumerated by the algorithm are interpreted as subtrees of a tree-decomposition that is constructed. This simplifies the proof of correctness and allows to discard subtrees from the enumeration by some simple observations. In our experiments, we show that one of these modifications in particular reduces the number of enumerated objects considerably. 2012 ACM Subject Classification Theory of computation → Fixed parameter tractability

[1] Linda C. van der Gaag,et al. Pre-processing for Triangulation of Probabilistic Networks , 2001, UAI.

[2] Arie M. C. A. Koster,et al. Treewidth computations II. Lower bounds , 2011, Inf. Comput..

[3] Hisao Tamaki. A heuristic use of dynamic programming to upperbound treewidth , 2019, ArXiv.

[4] Derek G. Corneil,et al. Complexity of finding embeddings in a k -tree , 1987 .

[5] Paul D. Seymour,et al. Graph Minors. II. Algorithmic Aspects of Tree-Width , 1986, J. Algorithms.

[6] Hans L. Bodlaender. A linear time algorithm for finding tree-decompositions of small treewidth , 1993, STOC '93.

[7] Kathryn Fraughnaugh,et al. Introduction to graph theory , 1973, Mathematical Gazette.

[8] Michal Pilipczuk,et al. A ck n 5-Approximation Algorithm for Treewidth , 2016, SIAM J. Comput..

[9] Ben Strasser,et al. Graph Bisection with Pareto Optimization , 2015, ALENEX.

[10] Ernst Althaus,et al. Optimal Tree Decompositions Revisited: A Simpler Linear-Time FPT Algorithm , 2019, ArXiv.

[11] Arie M. C. A. Koster,et al. Safe separators for treewidth , 2006, Discret. Math..

[12] Ioan Todinca,et al. Treewidth and Minimum Fill-in: Grouping the Minimal Separators , 2001, SIAM J. Comput..