Abstract
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 < 2. In this paper we show that such an algorithm with c = 1.9657 exists, and that there also exists an approximation algorithm and a constant τ such that an opt + τ approximation can be obtained in \(\mathcal{O}^*(1.89^ n)\) time.
This work is supported by the Research Council of Norway and by the Basal-CMM program of CONICYT, Chile.
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Suchan, K., Villanger, Y. (2009). Computing Pathwidth Faster Than 2n . In: Chen, J., Fomin, F.V. (eds) Parameterized and Exact Computation. IWPEC 2009. Lecture Notes in Computer Science, vol 5917. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11269-0_27
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DOI: https://doi.org/10.1007/978-3-642-11269-0_27
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