Journal ArticleDOI
Maximum Cardinality Search for Computing Minimal Triangulations of Graphs
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The new algorithm MCS-M combines the extension of L EX M with the simplification of MCS, achieving all the results of LEX M in the same time complexity.Abstract:
We present a new algorithm, called MCS-M, for computing minimal triangulations of graphs. Lex-BFS, a seminal algorithm for recognizing chordal graphs, was the genesis for two other classical algorithms: LEX M and MCS. LEX M extends the fundamental concept used in Lex-BFS, resulting in an algorithm that not only recognizes chordality, but also computes a minimal triangulation of an arbitrary graph. MCS simplifies the fundamental concept used in Lex-BFS, resulting in a simpler algorithm for recognizing chordal graphs. The new algorithm MCS-M combines the extension of LEX M with the simplification of MCS, achieving all the results of LEX M in the same time complexity.read more
Citations
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Journal ArticleDOI
Combinatorial Optimization on Graphs of Bounded Treewidth
TL;DR: The concepts of treewidth and tree decompositions are introduced, and the technique with the Weighted Independent Set problem is illustrated, to survey some of the latest developments.
Book
Chordal Graphs and Semidefinite Optimization
TL;DR: Thissurvey covers the theory and applications of chordal graphs, with anemphasis on algorithms developed in the literature on sparse Choleskyfactorization, and points out the connections with related topics outside semidefinite optimization, such as probabilistic networks, matrix completion problems, and partial separability in nonlinear optimization.
Journal ArticleDOI
Minimal triangulations of graphs: A survey
TL;DR: This survey presents and ties together a variety of algorithms for computing minimal triangulations of both general and restricted graph classes in a unified modern notation, keeping an emphasis on the algorithms.
Journal ArticleDOI
Treewidth computations I. Upper bounds
TL;DR: An overview of several upper bound heuristics that have been proposed and tested for the problem of determining the treewidth of a graph and finding tree decompositions and it is shown that in many cases, the heuristic give tree decomposition whose width is close to the exact treewitzer of the input graphs.
Book ChapterDOI
Discovering treewidth
TL;DR: This survey reviews algorithmic results on determining the treewidth of a given graph, and finding a tree decomposition of small width.
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