A measure & conquer approach for the analysis of exact algorithms
Journal of the ACM (JACM)
Strongly Chordal and Chordal Bipartite Graphs Are Sandwich Monotone
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
On the complexity of computing treelength
Discrete Applied Mathematics
On listing, sampling, and counting the chordal graphs with edge constraints
Theoretical Computer Science
Strongly chordal and chordal bipartite graphs are sandwich monotone
Journal of Combinatorial Optimization
Exact algorithm for the maximum induced planar subgraph problem
ESA'11 Proceedings of the 19th European conference on Algorithms
Subexponential parameterized algorithm for minimum fill-in
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Computing hypergraph width measures exactly
Information Processing Letters
A parameterized algorithm for chordal sandwich
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
On cutwidth parameterized by vertex cover
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
On exact algorithms for treewidth
ACM Transactions on Algorithms (TALG)
On the complexity of computing treelength
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
Decomposing combinatorial auctions and set packing problems
Journal of the ACM (JACM)
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We show that the treewidth and the minimum fill-in of an $n$-vertex graph can be computed in time $\mathcal{O}(1.8899^n)$. Our results are based on combinatorial proofs that an $n$-vertex graph has $\mathcal{O}(1.7087^n)$ minimal separators and $\mathcal{O}(1.8135^n)$ potential maximal cliques. We also show that for the class of asteroidal triple-free graphs the running time of our algorithms can be reduced to $\mathcal{O}(1.4142^n)$.