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
Exact Algorithms for Treewidth and Minimum Fill-In
SIAM Journal on Computing
Computing Pathwidth Faster Than 2n
Parameterized and Exact Computation
Treewidth computations I. Upper bounds
Information and Computation
New lower and upper bounds for graph treewidth
WEA'03 Proceedings of the 2nd international conference on Experimental and efficient algorithms
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
A space-time tradeoff for permutation problems
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Determinant Sums for Undirected Hamiltonicity
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations 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
A branch and bound algorithm for exact, upper, and lower bounds on treewidth
AAIM'06 Proceedings of the Second international conference on Algorithmic Aspects in Information and Management
SOFSEM'05 Proceedings of the 31st international conference on Theory and Practice of Computer Science
A Note on Exact Algorithms for Vertex Ordering Problems on Graphs
Theory of Computing Systems
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
On cutwidth parameterized by vertex cover
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
Computing directed pathwidth in O(1.89n) time
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
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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. We also consider the problem of computing Treewidth under the restriction that the space used is only polynomial and give a simple O*(4n) algorithm that requires polynomial space. We also show that with a more complicated algorithm using balanced separators, Treewidth can be computed in O*(2.9512n) time and polynomial space.