Abstract
The Minimum Size Tree Decomposition (MSTD) and Minimum Size Path Decomposition (MSPD) problems ask for a given nvertex 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/ log n) time and show that they cannot be solved in 2o(n/ log n) time, assuming the Exponential Time Hypothesis.
Cite
CITATION STYLE
Bodlaender, H. L., & Nederlof, J. (2015). Subexponential time algorithms for finding small tree and path decompositions. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9294, pp. 179–190). Springer Verlag. https://doi.org/10.1007/978-3-662-48350-3_16
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