Expected computation time for Hamiltonian path problem
SIAM Journal on Computing
Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
Listing all potential maximal cliques of a graph
Theoretical Computer Science
Treewidth and Minimum Fill-in: Grouping the Minimal Separators
SIAM Journal on Computing
Exact algorithms for NP-hard problems: a survey
Combinatorial optimization - Eureka, you shrink!
A complete anytime algorithm for treewidth
UAI '04 Proceedings of the 20th conference on Uncertainty in artificial intelligence
A practical algorithm for finding optimal triangulations
AAAI'97/IAAI'97 Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligence
SOFSEM'05 Proceedings of the 31st international conference on Theory and Practice of Computer Science
Degree-Based treewidth lower bounds
WEA'05 Proceedings of the 4th international conference on Experimental and Efficient Algorithms
New upper bound heuristics for treewidth
WEA'05 Proceedings of the 4th international conference on Experimental and Efficient Algorithms
Improved exponential-time algorithms for treewidth and minimum fill-in
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
Digraph measures: Kelly decompositions, games, and orderings
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Digraph measures: Kelly decompositions, games, and orderings
Theoretical Computer Science
Solving problems on recursively constructed graphs
ACM Computing Surveys (CSUR)
A measure & conquer approach for the analysis of exact algorithms
Journal of the ACM (JACM)
Best-first search for treewidth
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 2
Bandwidth of bipartite permutation graphs in polynomial time
Journal of Discrete Algorithms
Combining breadth-first and depth-first strategies in searching for treewidth
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Treewidth computations I. Upper bounds
Information and Computation
Treewidth: structure and algorithms
SIROCCO'07 Proceedings of the 14th international conference on Structural information and communication complexity
Exact structure discovery in Bayesian networks with less space
UAI '09 Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence
A space-time tradeoff for permutation problems
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Treewidth computations II. Lower bounds
Information and Computation
Exact algorithms for intervalizing colored graphs
TAPAS'11 Proceedings of the First international ICST conference on Theory and practice of algorithms in (computer) systems
Treewidth: characterizations, applications, and computations
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
A combinatorial optimization algorithm for solving the branchwidth problem
Computational Optimization and Applications
Finding optimal Bayesian networks using precedence constraints
The Journal of Machine Learning Research
TREEWIDTH and PATHWIDTH parameterized by the vertex cover number
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
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We give experimental and theoretical results on the problem of computing the treewidth of a graph by exact exponential time algorithms using exponential space or using only polynomial space. We first report on an implementation of a dynamic programming algorithm for computing the treewidth of a graph with running time O(2n). This algorithm is based on the old dynamic programming method introduced by Held and Karp for the TRAVELING SALESMAN problem. We use some optimizations that do not affect the worst case running time but improve on the running time on actual instances and can be seen to be practical for small instances. However, our experiments show that the space used by the algorithm is an important factor to what input sizes the algorithm is effective. For this purpose, we settle the problem of computing treewidth under the restriction that the space used is only polynomial. In this direction we give a simple O(4n) algorithm that requires polynomial space. We also prove that using more refined techniques with balanced separators, TREEWIDTH can be computed in O(2.9512n) time and polynomial space.