Depth-first iterative-deepening: an optimal admissible tree search
Artificial Intelligence
Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
Pre-processing for Triangulation of Probabilistic Networks
UAI '01 Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence
A complete anytime algorithm for treewidth
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Best-first search for treewidth
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 2
SOFSEM'05 Proceedings of the 31st international conference on Theory and Practice of Computer Science
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Depth-first search is effective at solving hard combinatorial problems, but if the problem space has a graph structure the same nodes may be searched many times. This can increase the size of the search exponentially. We explore two techniques that prevent this: duplicate detection and duplicate avoidance. We illustrate these techniques on the treewidth problem, a combinatorial optimization problem with applications to a variety of research areas. The bottleneck for previous treewidth algorithms is a large memory requirement. We develop a duplicate avoidance technique for treewidth and demonstrate that it significantly outperforms other algorithms when memory is limited. Additionally, we are able to find, for the first time, the treewidth of several hard benchmark graphs.