Journal ArticleDOI
Incremental modular decomposition
John H. Muller,Jeremy P. Spinrad +1 more
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TLDR
The time needed to find the modular decomposition of a graph is reduced by using less time to insert each vertex successively into the decomposition tree, using &Ogr;(<italic>n</italic>) time to inserting each vertex.Abstract:
Modular decomposition is a form of graph decomposition that has been discovered independently by researchers in graph theory, game theory, network theory, and other areas. This paper reduces the time needed to find the modular decomposition of a graph from O(n3) to O(n2). Together with a new algorithm for transitive orientation given in [21], this leads to fast new algorithms for a number of problems in graph recognition and isomorphism, including recognition of comparability graphs and permutation graphs. The new algorithm works by inserting each vertex successively into the decomposition tree, using O(n) time to insert each vertex.read more
Citations
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Book
Digraphs Theory Algorithms And Applications
Jrgen Bang-Jensen,Gregory Gutin +1 more
TL;DR: Digraphs is an essential, comprehensive reference for undergraduate and graduate students, and researchers in mathematics, operations research and computer science, and it will also prove invaluable to specialists in related areas, such as meteorology, physics and computational biology.
Sequencing and scheduling: algorithms and complexity
TL;DR: This survey focuses on the area of deterministic machine scheduling, and reviews complexity results and optimization and approximation algorithms for problems involving a single machine, parallel machines, open shops, flow shops and job shops.
Journal ArticleDOI
Upper bounds to the clique width of graphs
Bruno Courcelle,Stephan Olariu +1 more
TL;DR: Clique width is bound in terms of its tree width on the one hand, and of the clique width of its edge complement on the other, to reduce the complexity measure of graphs associated with hierarchical decompositions.
Book ChapterDOI
Chapter 9 Sequencing and scheduling: Algorithms and complexity
TL;DR: Different types of sequencing and scheduling problems are discussed, and different types of algorithms and the concepts of complexity theory are described.
Journal ArticleDOI
Modular decomposition and transitive orientation
TL;DR: This work gives O(n+m) algorithms for modular decomposition and transitive orientation, where n and m are the number of vertices and edges of the graph and linear time bounds for recognizing permutation graphs, maximum clique and minimum vertex coloring on comparability graphs, and other combinatorial problems on comparable graphs and their complements.
References
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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.
Journal ArticleDOI
A linear recognition algorithm for cographs
TL;DR: This paper presents a linear time algorithm for recognizing cographs and constructing their cotree representation, which is possible to design very fast polynomial time algorithms for problems which are intractable for graphs in general.
Book ChapterDOI
Substitution Decomposition for Discrete Structures and Connections with Combinatorial Optimization
TL;DR: In this paper, the substitution decomposition for Boolean functions, set systems and relations is studied and the results of the Jordan-Holder theorem and the uniqeness result for the associated composition tree are discussed.
Journal ArticleDOI
Decomposition of Directed Graphs
TL;DR: In this article, a general decomposition theory can be applied to the resulting digraph decomposition, a consequence is a theorem which asserts the uniqueness of a decomposition of any digraph, each member of the decomposition being either indecomposable or special.