Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
Listing all potential maximal cliques of a graph
Theoretical Computer Science
Treewidth and Minimum Fill-in: Grouping the Minimal Separators
SIAM Journal on Computing
A deterministic (2 - 2/(k+ 1))n algorithm for k-SAT based on local search
Theoretical Computer Science
Small Maximal Independent Sets and Faster Exact Graph Coloring
WADS '01 Proceedings of the 7th International Workshop on Algorithms and Data Structures
Exact algorithms for NP-hard problems: a survey
Combinatorial optimization - Eureka, you shrink!
Tour Merging via Branch-Decomposition
INFORMS Journal on Computing
Discrete Applied Mathematics - The 1st cologne-twente workshop on graphs and combinatorial optimization (CTW 2001)
Efficient approximation for triangulation of minimum treewidth
UAI'01 Proceedings of the Seventeenth conference on Uncertainty in artificial intelligence
On exact algorithms for treewidth
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
An exact algorithm for the minimum dominating clique problem
Theoretical Computer Science
Characterizing and Computing Minimal Cograph Completions
FAW '08 Proceedings of the 2nd annual international workshop on Frontiers in Algorithmics
A measure & conquer approach for the analysis of exact algorithms
Journal of the ACM (JACM)
Computing branchwidth via efficient triangulations and blocks
Discrete Applied Mathematics
Characterizing and computing minimal cograph completions
Discrete Applied Mathematics
Treewidth: structure and algorithms
SIROCCO'07 Proceedings of the 14th international conference on Structural information and communication complexity
Exact algorithms for edge domination
IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
An exact algorithm for the minimum dominating clique problem
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
On exact algorithms for treewidth
ACM Transactions on Algorithms (TALG)
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Exact exponential-time algorithms for NP-hard problems is an emerging field, and an increasing number of new results are being added continuously. Two important NP-hard problems that have been studied for decades are the treewidth and the minimum fill problems. Recently, an exact algorithm was presented by Fomin, Kratsch, and Todinca to solve both of these problems in time ${\mathcal O}^{*}$(1.9601n). Their algorithm uses the notion of potential maximal cliques, and is able to list these in time ${\mathcal O}^{*}$(1.9601n), which gives the running time for the above mentioned problems. We show that the number of potential maximal cliques for an arbitrary graph G on n vertices is ${\mathcal O}^{*}$(1.8135n), and that all potential maximal cliques can be listed in ${\mathcal O}^{*}$(1.8899n) time. As a consequence of this results, treewidth and minimum fill-in can be computed in ${\mathcal O}^{*}$(1.8899n) time.