Abstract
The Minimum Size Tree Decomposition (MSTD) and Minimum Size Path Decomposition (MSPD) problems ask for a given n-vertex graph G and integer k, what is the minimum number of bags of a tree decomposition (respectively, path decomposition) of width at most k. The problems are known to be NP-complete for each fixed k ≥ 4. In this paper we present algorithms that solve both problems for fixed k in 2O(n/ logn) time and show that they cannot be solved in 2o(n / logn) time, assuming the Exponential Time Hypothesis.
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Bodlaender, H.L., Nederlof, J. (2015). Subexponential Time Algorithms for Finding Small Tree and Path Decompositions. In: Bansal, N., Finocchi, I. (eds) Algorithms - ESA 2015. Lecture Notes in Computer Science(), vol 9294. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48350-3_16
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DOI: https://doi.org/10.1007/978-3-662-48350-3_16
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