Computational Graph Theory
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Computational Graph Theory
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Author : Rudolf Albrecht
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Computational Graph Theory written by Rudolf Albrecht and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Computers categories.
One ofthe most important aspects in research fields where mathematics is "applied is the construction of a formal model of a real system. As for structural relations, graphs have turned out to provide the most appropriate tool for setting up the mathematical model. This is certainly one of the reasons for the rapid expansion in graph theory during the last decades. Furthermore, in recent years it also became clear that the two disciplines of graph theory and computer science have very much in common, and that each one has been capable of assisting significantly in the development of the other. On one hand, graph theorists have found that many of their problems can be solved by the use of com puting techniques, and on the other hand, computer scientists have realized that many of their concepts, with which they have to deal, may be conveniently expressed in the lan guage of graph theory, and that standard results in graph theory are often very relevant to the solution of problems concerning them. As a consequence, a tremendous number of publications has appeared, dealing with graphtheoretical problems from a computational point of view or treating computational problems using graph theoretical concepts.
Graph Theory And Computing
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Author : Ronald C. Read
language : en
Publisher: Academic Press
Release Date : 2014-05-12
Graph Theory And Computing written by Ronald C. Read and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-12 with Mathematics categories.
Graph Theory and Computing focuses on the processes, methodologies, problems, and approaches involved in graph theory and computer science. The book first elaborates on alternating chain methods, average height of planted plane trees, and numbering of a graph. Discussions focus on numbered graphs and difference sets, Euclidean models and complete graphs, classes and conditions for graceful graphs, and maximum matching problem. The manuscript then elaborates on the evolution of the path number of a graph, production of graphs by computer, and graph-theoretic programming language. Topics include FORTRAN characteristics of GTPL, design considerations, representation and identification of graphs in a computer, production of simple graphs and star topologies, and production of stars having a given topology. The manuscript examines the entropy of transformed finite-state automata and associated languages; counting hexagonal and triangular polyominoes; and symmetry of cubical and general polyominoes. Graph coloring algorithms, algebraic isomorphism invariants for graphs of automata, and coding of various kinds of unlabeled trees are also discussed. The publication is a valuable source of information for researchers interested in graph theory and computing.
Graph Based Knowledge Representation
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Author : Michel Chein
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-10-20
Graph Based Knowledge Representation written by Michel Chein and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-20 with Mathematics categories.
This book provides a de?nition and study of a knowledge representation and r- soning formalism stemming from conceptual graphs, while focusing on the com- tational properties of this formalism. Knowledge can be symbolically represented in many ways. The knowledge representation and reasoning formalism presented here is a graph formalism – knowledge is represented by labeled graphs, in the graph theory sense, and r- soning mechanisms are based on graph operations, with graph homomorphism at the core. This formalism can thus be considered as related to semantic networks. Since their conception, semantic networks have faded out several times, but have always returned to the limelight. They faded mainly due to a lack of formal semantics and the limited reasoning tools proposed. They have, however, always rebounded - cause labeled graphs, schemas and drawings provide an intuitive and easily und- standable support to represent knowledge. This formalism has the visual qualities of any graphic model, and it is logically founded. This is a key feature because logics has been the foundation for knowledge representation and reasoning for millennia. The authors also focus substantially on computational facets of the presented formalism as they are interested in knowledge representation and reasoning formalisms upon which knowledge-based systems can be built to solve real problems. Since object structures are graphs, naturally graph homomorphism is the key underlying notion and, from a computational viewpoint, this moors calculus to combinatorics and to computer science domains in which the algorithmicqualitiesofgraphshavelongbeenstudied,asindatabasesandconstraint networks.
Graph Theory And Sparse Matrix Computation
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Author : Alan George
language : en
Publisher: Springer
Release Date : 2011-10-24
Graph Theory And Sparse Matrix Computation written by Alan George and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-24 with Mathematics categories.
This IMA Volume in Mathematics and its Appllcations GRAPH THEORY AND SPARSE MATRIX COMPUTATION is based on the proceedings of a workshop that was an integraI part of the 1991- 92 IMA program on "Applied Linear AIgebra." The purpose of the workshop was to bring together people who work in sparse matrix computation with those who conduct research in applied graph theory and grl: l, ph algorithms, in order to foster active cross-fertilization. We are grateful to Richard Brualdi, George Cybenko, Alan Geo ge, Gene Golub, Mitchell Luskin, and Paul Van Dooren for planning and implementing the year-Iong program. We espeeially thank Alan George, John R. Gilbert, and Joseph W.H. Liu for organizing this workshop and editing the proceedings. The finaneial support of the National Science Foundation made the workshop possible. A vner Friedman Willard Miller. Jr. PREFACE When reality is modeled by computation, linear algebra is often the con nec- tiori between the continuous physical world and the finite algorithmic one. Usually, the more detailed the model, the bigger the matrix, the better the answer. Efficiency demands that every possible advantage be exploited: sparse structure, advanced com- puter architectures, efficient algorithms. Therefore sparse matrix computation knits together threads from linear algebra, parallei computing, data struetures, geometry, and both numerieal and discrete algorithms.
Some Topics In Graph Theory
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Author : Hian Poh Yap
language : en
Publisher: Cambridge University Press
Release Date : 1986-07-17
Some Topics In Graph Theory written by Hian Poh Yap and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986-07-17 with Mathematics categories.
This book provides a rapid introduction to topics in graph theory typically covered in a graduate course. The author sets out the main recent results in several areas of current research in graph theory. Topics covered include edge-colourings, symmetries of graphs, packing of graphs, and computational complexity. Professor Yap is able to lead the reader to the forefront of research and to describe some of the open problems in the field. The choice of material presented has arisen from courses given at the National University of Singapore and each chapter contains numerous examples and exercises for the reader.
Applied Graph Theory In Computer Vision And Pattern Recognition
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Author : Abraham Kandel
language : en
Publisher: Springer
Release Date : 2007-04-11
Applied Graph Theory In Computer Vision And Pattern Recognition written by Abraham Kandel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-11 with Technology & Engineering categories.
Graph theory has strong historical roots in mathematics, especially in topology. Its birth is usually associated with the “four-color problem” posed by Francis Guthrie 1 in 1852, but its real origin probably goes back to the Seven Bridges of Konigsber ̈ g 2 problem proved by Leonhard Euler in 1736. A computational solution to these two completely different problems could be found after each problem was abstracted to the level of a graph model while ignoring such irrelevant details as country shapes or cross-river distances. In general, a graph is a nonempty set of points (vertices) and the most basic information preserved by any graph structure refers to adjacency relationships (edges) between some pairs of points. In the simplest graphs, edges do not have to hold any attributes, except their endpoints, but in more sophisticated graph structures, edges can be associated with a direction or assigned a label. Graph vertices can be labeled as well. A graph can be represented graphically as a drawing (vertex=dot,edge=arc),but,aslongaseverypairofadjacentpointsstaysconnected by the same edge, the graph vertices can be moved around on a drawing without changing the underlying graph structure. The expressive power of the graph models placing a special emphasis on c- nectivity between objects has made them the models of choice in chemistry, physics, biology, and other ?elds.
Computational Discrete Mathematics
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Author : Sriram Pemmaraju
language : en
Publisher: Cambridge University Press
Release Date : 2003-12-08
Computational Discrete Mathematics written by Sriram Pemmaraju and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-12-08 with Computers categories.
This definitive reference on Combinatorica contains examples of all 450 functions plus tutorial text.
Analysis Of Biological Data A Soft Computing Approach
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Author : Sanghamitra Bandyopadhyay
language : en
Publisher: World Scientific
Release Date : 2007-09-03
Analysis Of Biological Data A Soft Computing Approach written by Sanghamitra Bandyopadhyay and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-09-03 with Computers categories.
Bioinformatics, a field devoted to the interpretation and analysis of biological data using computational techniques, has evolved tremendously in recent years due to the explosive growth of biological information generated by the scientific community. Soft computing is a consortium of methodologies that work synergistically and provides, in one form or another, flexible information processing capabilities for handling real-life ambiguous situations. Several research articles dealing with the application of soft computing tools to bioinformatics have been published in the recent past; however, they are scattered in different journals, conference proceedings and technical reports, thus causing inconvenience to readers, students and researchers.This book, unique in its nature, is aimed at providing a treatise in a unified framework, with both theoretical and experimental results, describing the basic principles of soft computing and demonstrating the various ways in which they can be used for analyzing biological data in an efficient manner. Interesting research articles from eminent scientists around the world are brought together in a systematic way such that the reader will be able to understand the issues and challenges in this domain, the existing ways of tackling them, recent trends, and future directions. This book is the first of its kind to bring together two important research areas, soft computing and bioinformatics, in order to demonstrate how the tools and techniques in the former can be used for efficiently solving several problems in the latter.
Topics In Intersection Graph Theory
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Author : Terry A. McKee
language : en
Publisher: SIAM
Release Date : 1999-01-01
Topics In Intersection Graph Theory written by Terry A. McKee and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-01-01 with Mathematics categories.
Finally there is a book that presents real applications of graph theory in a unified format. This book is the only source for an extended, concentrated focus on the theory and techniques common to various types of intersection graphs. It is a concise treatment of the aspects of intersection graphs that interconnect many standard concepts and form the foundation of a surprising array of applications to biology, computing, psychology, matrices, and statistics.