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Journals ACM Computing Surveys (CSUR) Volume 41 Issue 1

Solving Problems on Recursively Constructed Graphs RICHARD B. BORIE University of Alabama and R. GARY PARKER and CRAIG A. TOVEY Georgia Institute of Technology Fast algorithms can be created for many graph problems when instances are con ned to classes of graphs that are recursively constructed. This article rst describes some basic conceptual notions regarding the design of such fast algorithms, and then the coverage proceeds through several recursive graph classes. Speci c classes include trees, series-parallel graphs, k-terminal graphs, treewidth-k graphs, k-trees, partial k-trees, k-jackknife graphs, pathwidth-k graphs, bandwidth-k graphs, cutwidth-k graphs, branchwidth-k graphs, Halin graphs, cographs, cliquewidth-k graphs, k-NLC graphs, k-HB graphs, and rankwidth-k graphs. The de nition of each class is provided. Typical algorithms are applied to solve problems on instances of most classes. Relationships between the classes are also discussed. Categories and Subject Descriptors: G.2.2 [Discrete Mathematics]: Graph Theory; F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and Problems General Terms: Algorithms, Theory Additional Key Words and Phrases: Bandwidth, branchwidth, cliquewidth, cograph, cutwidth, dynamic programming, Halin graph, pathwidth, rankwidth, series parallel, tree, treewidth ACM Reference Format: Borie, R. B., Parker, R. G., and Tovey, C. A. 2008. Solving problems on recursively constructed graphs.

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Solving problems on recursively constructed graphs

Borie, Richard B.; Parker, R. Gary; Tovey, Craig A.
ACM Computing Surveys (CSUR) , Volume 41 (1)
Association for Computing Machinery – Dec 1, 2008

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