Efficient and Constructive Algorithms for the Pathwidth and Treewidth of Graphs
Hans L. Bodlaender,Ton Kloks +1 more
TL;DR: For all constantsk,l, explicit algorithms that, given a graphG=(V,E) with a tree-decomposition ofG with treewidth with useO(|V|) time are given, which do not rely on non-constructive reasoning and are single exponential inkandl.
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About: This article is published in Journal of Algorithms. The article was published on 01 Sep 1996. and is currently open access. The article focuses on the topics: Tree decomposition & Tree-depth.
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Citations
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Parameterized Algorithms
Marek Cygan,Fedor V. Fomin,Lukasz Kowalik,Daniel Lokshtanov,Dániel Marx,Marcin Pilipczuk,Michał Pilipczuk,Saket Saurabh +7 more
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TL;DR: This comprehensive textbook presents a clean and coherent account of most fundamental tools and techniques in Parameterized Algorithms and is a self-contained guide to the area, providing a toolbox of algorithmic techniques.
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A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
TL;DR: Every minor-closed class of graphs that does not contain all planar graphs has a linear-time recognition algorithm that determines whether the treewidth of G is at most at most some constant $k$ and finds a tree-decomposition of G withtreewidth at most k.
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Graph Structure and Monadic Second-Order Logic: A Language-Theoretic Approach
Bruno Courcelle,Joost Engelfriet +1 more
- 23 Jul 2012
TL;DR: The author not only provides a thorough description of the theory, but also details its applications, on the one hand to the construction of graph algorithms, and the extension of formal language theory to finite graphs.
Treewidth: Algorithmic techniques and results
Hans L. Bodlaender
- 25 Aug 1997
TL;DR: This paper gives an overview of several results and techniques for graphs algorithms that compute the treewidth of a graph or that solve otherwise intractable problems when restricted graphs with boundedtreewidth more efficiently.
346
A $c^k n$ 5-Approximation Algorithm for Treewidth
Hans L. Bodlaender,Pål Grǿnås Drange,Markus Sortland Dregi,Fedor V. Fomin,Daniel Lokshtanov,Michał Pilipczuk +5 more
TL;DR: This is the first algorithm providing a constant factor approximation for treewidth which runs in time single exponential in $k$ and linear in the input size and can be used to speed up many algorithms to work in time.
277
References
Local computations with probabilities on graphical structures and their application to expert systems
TL;DR: The invention comprises pigments of the general Formula I in which each X is hydrogen, chlorine or bromine, A is (a) an aliphatic hydrocarbon radical, (b) the phenylene group or (c) the naphthylene group and R is identical with the 1: 2-phthaloylcarbazole-aminocarbonyl radical shown in the formula.
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Graph minors. II: Algorithmic aspects of tree-width
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