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)
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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Computing the Pathwidth of a graph is the problem of finding a tree decomposition of minimum width, where the decomposition tree is a path. It can be easily computed in $\mathcal{O}^*(2^n)$ time by using dynamic programming over all vertex subsets. For some time now there has been an open problem if there exists an algorithm computing Pathwidth with running time $\mathcal{O}^*(c^n)$ for c c = 1.9657 exists, and that there also exists an approximation algorithm and a constant 驴 such that an opt + 驴 approximation can be obtained in $\mathcal{O}^*(1.89^ n)$ time.