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John H. Muller

Bio: John H. Muller is an academic researcher from University of Toronto. The author has contributed to research in topics: Symmetric graph & Modular decomposition. The author has an hindex of 1, co-authored 1 publications receiving 112 citations.

Papers
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Journal ArticleDOI
TL;DR: 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;(n) 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.

114 citations


Cited by
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Book
05 Aug 2002
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.
Abstract: The theory of directed graphs has developed enormously over recent decades, yet this book (first published in 2000) remains the only book to cover more than a small fraction of the results. New research in the field has made a second edition a necessity. Substantially revised, reorganised and updated, the book now comprises eighteen chapters, carefully arranged in a straightforward and logical manner, with many new results and open problems. As well as covering the theoretical aspects of the subject, with detailed proofs of many important results, the authors present a number of algorithms, and whole chapters are devoted to topics such as branchings, feedback arc and vertex sets, connectivity augmentations, sparse subdigraphs with prescribed connectivity, and also packing, covering and decompositions of digraphs. Throughout the book, there is a strong focus on applications which include quantum mechanics, bioinformatics, embedded computing, and the travelling salesman problem. Detailed indices and topic-oriented chapters ease navigation, and more than 650 exercises, 170 figures and 150 open problems are included to help immerse the reader in all aspects of the subject. Digraphs is an essential, comprehensive reference for undergraduate and graduate students, and researchers in mathematics, operations research and computer science. It will also prove invaluable to specialists in related areas, such as meteorology, physics and computational biology.

1,938 citations

01 Jan 1989
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.

1,401 citations

Journal ArticleDOI
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.

707 citations

Book ChapterDOI
01 Jan 1993
TL;DR: Different types of sequencing and scheduling problems are discussed, and different types of algorithms and the concepts of complexity theory are described.
Abstract: Publisher Summary This chapter discusses different types of sequencing and scheduling problems, and describes different types of algorithms and the concepts of complexity theory. A class of deterministic machine scheduling problems has been introduced in the chapter. The chapter also deals with the single machine, parallel machine and multi-operation problems in this class, respectively. The two generalizations of the deterministic machine-scheduling model have been presented in the chapter. A deterministic scheduling model may give rise to various stochastic counterparts, as there is a choice in the parameters that are randomized, in their distributions, and in the classes of policies that can be applied. A characteristic feature of these models is that the stochastic parameters are regarded as independent random variables with a given distribution and that their realization occurs only after the scheduling decision has been made. In the deterministic model, one has perfect information, and capitalizing on it in minimizing the realization of a performance measure may require exponential time.

551 citations

Journal ArticleDOI
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.

450 citations