A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
A comparison of structural CSP decomposition methods
Artificial Intelligence
Tree Decomposition Based Fast Search of RNA Structures Including Pseudoknots in Genomes
CSB '05 Proceedings of the 2005 IEEE Computational Systems Bioinformatics Conference
Finding Branch-Decompositions and Rank-Decompositions
SIAM Journal on Computing
Treewidth computations I. Upper bounds
Information and Computation
On the Boolean-width of a graph: structure and applications
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
A local search algorithm for branchwidth
SOFSEM'11 Proceedings of the 37th international conference on Current trends in theory and practice of computer science
Treewidth computations II. Lower bounds
Information and Computation
Treewidth: characterizations, applications, and computations
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Graph classes with structured neighborhoods and algorithmic applications
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
A SAT approach to clique-width
SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
Fast dynamic programming for locally checkable vertex subset and vertex partitioning problems
Theoretical Computer Science
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It is well-known that for graphs with high edge density the tree-width is always high while the clique-width can be low. Boolean-width is a new parameter that is never higher than tree-width or clique-width and can in fact be as small as logarithmic in clique-width. Boolean-width is defined using a decomposition tree by evaluating the number of neighborhoods across the resulting cuts of the graph. Several NP-hard problems can be solved efficiently by dynamic programming when given a decomposition of boolean-width k, e.g. Max Weight Independent Set in time O(n2k22k) and Min Weight Dominating Set in time O(n2+nk23k). Finding decompositions of low boolean-width is therefore of practical interest. There is evidence that computing boolean-width is hard, while the existence of a useful approximation algorithm is still open. In this paper we introduce and study a heuristic algorithm that finds a reasonably good decomposition to be used for dynamic programming based on boolean-width. On a set of graphs of practical relevance, specifically graphs in TreewidthLIB, the best known upper bound on their tree-width is compared to the upper bound on their boolean-width given by our heuristic. For the large majority of the graphs on which we made the tests, the tree-width bound is at least twice as big as the boolean-width bound, and boolean-width compares better the higher the edge density. This means that, for problems like Dominating Set, using boolean-width should outperform dynamic programming by tree-width, at least for graphs of edge density above a certain bound. In view of the amount of previous work on heuristics for tree-width these results indicate that boolean-width could in the future outperform tree-width in practice for a large class of graphs and problems.