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Author: Vadim Zverovich
Publisher: Oxford University Press
ISBN: 0198882106
Category : Mathematics
Languages : en
Pages : 289
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Book Description
In general terms, a graph decomposition is a partition of a graph into parts satisfying some special conditions. Methods of Graph Decompositions discusses some state-of-the-art decomposition methods of graph theory, which are highly instrumental when dealing with a number of fundamental concepts such as unigraphs, isomorphism, reconstruction conjectures, k-dimensional graphs, degree sequences, line graphs and line hypergraphs. The first part of the book explores the algebraic theory of graph decomposition, whose major idea is to define a binary operation that turns the set of graphs or objects derived from graphs into an algebraic semigroup. If an operation and a class of graphs are appropriately chosen, then, just as for integers, each graph has a unique factorization (or canonical decomposition) into a product of prime factors. The unique factorization property makes this type of decomposition especially efficient for problems associated with graph isomorphism, and several such examples are described in the book. Another topic is devoted to Krausz-type decompositions, that is, special coverings of graphs by cliques that are directly associated with representation of graphs as line graphs of hypergraphs. The book discusses various algorithmic and structural results associated with the existence, properties and applications of such decompositions. In particular, it demonstrates how Krausz-type decompositions are directly related to topological dimension, information complexity and self-similarity of graphs, thus allowing to establish links between combinatorics, general topology, information theory and studies of complex systems. The above topics are united by the role played in their development by Professor Regina Tyshkevich, and the book is a tribute to her memory. The book will be ideal for researchers, engineers and specialists, who are interested in fundamental problems of graph theory and proof techniques to tackle them.
Author: Vadim Zverovich
Publisher: Oxford University Press
ISBN: 0198882106
Category : Mathematics
Languages : en
Pages : 289
Get Book Here
Book Description
In general terms, a graph decomposition is a partition of a graph into parts satisfying some special conditions. Methods of Graph Decompositions discusses some state-of-the-art decomposition methods of graph theory, which are highly instrumental when dealing with a number of fundamental concepts such as unigraphs, isomorphism, reconstruction conjectures, k-dimensional graphs, degree sequences, line graphs and line hypergraphs. The first part of the book explores the algebraic theory of graph decomposition, whose major idea is to define a binary operation that turns the set of graphs or objects derived from graphs into an algebraic semigroup. If an operation and a class of graphs are appropriately chosen, then, just as for integers, each graph has a unique factorization (or canonical decomposition) into a product of prime factors. The unique factorization property makes this type of decomposition especially efficient for problems associated with graph isomorphism, and several such examples are described in the book. Another topic is devoted to Krausz-type decompositions, that is, special coverings of graphs by cliques that are directly associated with representation of graphs as line graphs of hypergraphs. The book discusses various algorithmic and structural results associated with the existence, properties and applications of such decompositions. In particular, it demonstrates how Krausz-type decompositions are directly related to topological dimension, information complexity and self-similarity of graphs, thus allowing to establish links between combinatorics, general topology, information theory and studies of complex systems. The above topics are united by the role played in their development by Professor Regina Tyshkevich, and the book is a tribute to her memory. The book will be ideal for researchers, engineers and specialists, who are interested in fundamental problems of graph theory and proof techniques to tackle them.
Author: Reinhard Diestel
Publisher: Oxford Science Publications
ISBN:
Category : Language Arts & Disciplines
Languages : en
Pages : 258
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Book Description
Graph Decompositions is the first book on a topic that belongs mainly to infinite graph theory. It offers a complete account of the theory of simplicial decompositions of graphs, from its origins in the 1930s right up to present-day research.In addition to being one of the most important tools in infinite graph theory, simplicial decompositions may be seen as a model for any kind of structural graph decomposition. The currently topical tree-decompositions, for example, have their origin in simplicial decompositions.The text is centred around a few guiding problems and concepts, such as the existence and the uniqueness problem of simplicial decompositions into primes, or the concept of excluded minors as a means of identifying a desired structure.It attempts to give as authentic a picture as possible ofresearch in progress. To this end, it includes discussions of examples, proof strategies on the formation of new concepts, as well as numerous exercises and open problems.Graph Decompositions should prove attractive to any graph theorist or other mathematician interested in a new area of research, as well as to the advanced student looking for a lively and inspiring account of how such research evolves.
Author: José L. Balcázar
Publisher: Springer Science & Business Media
ISBN: 364215882X
Category : Computers
Languages : en
Pages : 538
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Book Description
This book constitutes the refereed proceedings of the joint conference on Machine Learning and Knowledge Discovery in Databases: ECML PKDD 2010, held in Barcelona, Spain, in September 2010. The 120 revised full papers presented in three volumes, together with 12 demos (out of 24 submitted demos), were carefully reviewed and selected from 658 paper submissions. In addition, 7 ML and 7 DM papers were distinguished by the program chairs on the basis of their exceptional scientific quality and high impact on the field. The conference intends to provide an international forum for the discussion of the latest high quality research results in all areas related to machine learning and knowledge discovery in databases. A topic widely explored from both ML and DM perspectives was graphs, with motivations ranging from molecular chemistry to social networks.
Author: Irfan M. Ovacik
Publisher: Springer Science & Business Media
ISBN: 1461563291
Category : Business & Economics
Languages : en
Pages : 217
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Book Description
The factory scheduling problem, that of allocating machines to competing jobs in manufacturing facilities to optimize or at least improve system performance, is encountered in many different manufacturing environments. Given the competitive pressures faced by many companies in today's rapidly changing global markets, improved factory scheduling should contribute to a flrm's success. However, even though an extensive body of research on scheduling models has been in existence for at least the last three decades, most of the techniques currently in use in industry are relatively simplistic, and have not made use of this body of knowledge. In this book we describe a systematic, long-term research effort aimed at developing effective scheduling algorithms for complex manufacturing facilities. We focus on a speciflc industrial context, that of semiconductor manufacturing, and try to combine knowledge of the physical production system with the methods and results of scheduling research to develop effective approximate solution procedures for these problems. The class of methods we suggest, decomposition methods, constitute a broad family of heuristic approaches to large, NP-hard scheduling problems which can be applied in other environments in addition to those studied in this book.
Author: L. Døvling Andersen
Publisher: Elsevier
ISBN: 0080867812
Category : Mathematics
Languages : en
Pages : 533
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Book Description
This volume is a tribute to the life and mathematical work of G.A. Dirac (1925-1984). One of the leading graph theorists, he developed methods of great originality and made many fundamental discoveries.The forty-two papers are all concerned with (or related to) Dirac's main lines of research. A number of mathematicians pay tribute to his memory by presenting new results in different areas of graph theory. Among the topics included are paths and cycles, hamiltonian graphs, vertex colouring and critical graphs, graphs and surfaces, edge-colouring, and infinite graphs.Some of the papers were originally presented at a meeting held in Denmark in 1985. Attendance being by invitation only, some 55 mathematicians from 14 countries participated in various lectures and discussions on graph theory related to the work of Dirac. This volume contains contributions from others as well, so should not be regarded only as the proceedings of that meeting. A problems section is included, as well as a listing of Dirac's own publications.
Author: Gary Chartrand
Publisher: Courier Corporation
ISBN: 0486297306
Category : Mathematics
Languages : en
Pages : 466
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Book Description
Written by two prominent figures in the field, this comprehensive text provides a remarkably student-friendly approach. Its sound yet accessible treatment emphasizes the history of graph theory and offers unique examples and lucid proofs. 2004 edition.
Author: Lieven Vandenberghe
Publisher: Foundations and Trends (R) in Optimization
ISBN: 9781680830385
Category :
Languages : en
Pages : 216
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Book Description
Covers the theory and applications of chordal graphs, with an emphasis on algorithms developed in the literature on sparse Cholesky factorization. It shows how these techniques can be applied in algorithms for sparse semidefinite optimization, and points out the connections with related topics outside semidefinite optimization.
Author: Bruno Courcelle
Publisher: Cambridge University Press
ISBN: 1139644009
Category : Mathematics
Languages : en
Pages : 743
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Book Description
The study of graph structure has advanced in recent years with great strides: finite graphs can be described algebraically, enabling them to be constructed out of more basic elements. Separately the properties of graphs can be studied in a logical language called monadic second-order logic. In this book, these two features of graph structure are brought together for the first time in a presentation that unifies and synthesizes research over the last 25 years. The authors not only provide a thorough description of the theory, but also detail its applications, on the one hand to the construction of graph algorithms, and, on the other to the extension of formal language theory to finite graphs. Consequently the book will be of interest to graduate students and researchers in graph theory, finite model theory, formal language theory, and complexity theory.
Author: D. A. Holton
Publisher: Cambridge University Press
ISBN: 0521435943
Category : Mathematics
Languages : en
Pages : 367
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Book Description
The authors examine various areas of graph theory, using the prominent role of the Petersen graph as a unifying feature.
Author: Jeremy Kepner
Publisher: SIAM
ISBN: 9780898719918
Category : Mathematics
Languages : en
Pages : 388
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Book Description
The current exponential growth in graph data has forced a shift to parallel computing for executing graph algorithms. Implementing parallel graph algorithms and achieving good parallel performance have proven difficult. This book addresses these challenges by exploiting the well-known duality between a canonical representation of graphs as abstract collections of vertices and edges and a sparse adjacency matrix representation. This linear algebraic approach is widely accessible to scientists and engineers who may not be formally trained in computer science. The authors show how to leverage existing parallel matrix computation techniques and the large amount of software infrastructure that exists for these computations to implement efficient and scalable parallel graph algorithms. The benefits of this approach are reduced algorithmic complexity, ease of implementation, and improved performance.
