Algorithms for generalized vertex-rankings of partial k -trees
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This work presents sequential and parallel algorithms to find an optimal c -vertex-ranking of a partial k -tree, that is, a graph of treewidth bounded by a fixed integer k .About:
This article is published in Theoretical Computer Science.The article was published on 2000-06-17 and is currently open access. It has received 23 citations till now. The article focuses on the topics: Path graph & Graph toughness.read more
Citations
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BookDOI
The Multivariate Algorithmic Revolution and Beyond
TL;DR: Through the hazy lens of (my) memory, this work will try to reconstruct how Mike Fellows and I, together with some co-authors in some cases, came up with the basic papers in parameterized complexity.
Journal ArticleDOI
The Behavior of Clique-Width under Graph Operations and Graph Transformations
TL;DR: This paper gives upper and lower bounds for the clique-width and NLC-width of the modified graphs in terms of the cliques- width and N LC- width of the involved graphs.
Journal ArticleDOI
Solving problems on recursively constructed graphs
TL;DR: This article first describes some basic conceptual notions regarding the design of such fast algorithms, and then the coverage proceeds through several recursive graph classes, which include trees, series-parallel graphs, and treewidth-k graphs.
Book ChapterDOI
Fixed-Parameter tractability of treewidth and pathwidth
TL;DR: In this survey, a number of results on the fixed-parameter tractability of treewidth and pathwidth are discussed and a linear-time algorithm for testing if a graph has pathwidth at most some given constant is discussed in more detail.
Posted Content
A comparison of two approaches for polynomial time algorithms computing basic graph parameters
TL;DR: This paper gives polynomial time algorithms for computing the four basic graph parameters independence number, clique number, chromatic number, and clique covering number on a given tree structure of graphs of bounded tree-width and graph of bounded clique-width in polynometric time.
References
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Journal ArticleDOI
Graph minors. II: Algorithmic aspects of tree-width
Neil Robertson,Paul Seymour +1 more
TL;DR: An invariant of graphs called the tree-width is introduced, and used to obtain a polynomially bounded algorithm to test if a graph has a subgraph contractible to H, where H is any fixed planar graph.
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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.
Book
An introduction to parallel algorithms
TL;DR: This book provides an introduction to the design and analysis of parallel algorithms, with the emphasis on the application of the PRAM model of parallel computation, with all its variants, to algorithm analysis.
Journal ArticleDOI
The Multifrontal Solution of Indefinite Sparse Symmetric Linear
Iain S. Duff,John Reid +1 more
TL;DR: On etend la methode frontale pour resoudre des systemes lineaires d'equations en permettant a plus d'un front d'apparaitre en meme temps.
Journal ArticleDOI
The role of elimination trees in sparse factorization
TL;DR: The role of elimination trees in the direct solution of large sparse linear systems is examined and its relation to sparse Cholesky factorization is discussed.