Abstract
We present a modification of Bodlaender’s linear time algorithm that, for constant k, determines whether an input graph G = (V,E) has treewidth k and, if so, constructs a tree decomposition of G of width at most k. Our algorithm has the following additional feature: if G has treewidth greater than k then a subgraph G′ of G of treewidth greater than k is returned along with a tree decomposition of G′ of width at most 2k. A consequence is that the fundamental disjoint rooted paths problem can now be solved in O(n2) time. This is the primary motivation for this paper.
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© 1999 Springer-Verlag Berlin Heidelberg
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Perković, L., Reed, B. (1999). An Improved Algorithm for Finding Tree Decompositions of Small Width. In: Widmayer, P., Neyer, G., Eidenbenz, S. (eds) Graph-Theoretic Concepts in Computer Science. WG 1999. Lecture Notes in Computer Science, vol 1665. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46784-X_15
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DOI: https://doi.org/10.1007/3-540-46784-X_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66731-5
Online ISBN: 978-3-540-46784-7
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