Book ChapterDOI
Graph Problems Related to Gate Matrix Layout and PLA Folding
Rolf H. Möhring
- Iss: 7, pp 17-51
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TLDR
A survey on graph problems occuring in linear VLSI layout architectures such as gate matrix layout, folding of programmable logic arrays, and Weinberger arrays and results presented include NP-hardness of gate Matrix layout on chordal graphs, efficient algorithms for trees, cographs, and certain chordal graph graphs, Lagrangean relaxation and approximation algorithms based on on-line interval graph augmentation.Citations
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Journal ArticleDOI
A partial k -arboretum of graphs with bounded treewidth
TL;DR: This survey paper wants to give an overview of many classes of graphs that can be seen to have a uniform upper bound on the treewidth of graphs in the class.
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A tourist guide through treewidth
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An annotated bibliography on guaranteed graph searching
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Approximating treewidth, pathwidth, frontsize, and shortest elimination tree
TL;DR: Various parameters of graphs connected to sparse matrix factorization and other applications can be approximated using an algorithm of Leighton et al. that finds vertex separators of graphs, and it is shown that unless P = NP there are no absolute approximation algorithms for any of the parameters.
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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.
References
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Book
Computers and Intractability: A Guide to the Theory of NP-Completeness
TL;DR: The second edition of a quarterly column as discussed by the authors provides a continuing update to the list of problems (NP-complete and harder) presented by M. R. Garey and myself in our book "Computers and Intractability: A Guide to the Theory of NP-Completeness,” W. H. Freeman & Co., San Francisco, 1979.
Book
Algorithmic graph theory and perfect graphs
TL;DR: This new Annals edition continues to convey the message that intersection graph models are a necessary and important tool for solving real-world problems and remains a stepping stone from which the reader may embark on one of many fascinating research trails.
A guide to the theory of np-completeness
TL;DR: This is the second edition of a quarterly column the purpose of which is to provide a continuing update to the list of problems (NP-complete and harder) presented by M. R. Garey and myself in the authors' book ‘‘Computers and Intractability: A Guide to the Theory of NP-Completeness’’.
Journal ArticleDOI
Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms
TL;DR: The consecutive ones test for the consecutive ones property in matrices and for graph planarity is extended to a test for interval graphs using a recently discovered fast recognition algorithm for chordal graphs.