Download or read book A Guide to Graph Colouring written by R.M.R. Lewis and published by Springer. This book was released on 2015-10-26 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book treats graph colouring as an algorithmic problem, with a strong emphasis on practical applications. The author describes and analyses some of the best-known algorithms for colouring arbitrary graphs, focusing on whether these heuristics can provide optimal solutions in some cases; how they perform on graphs where the chromatic number is unknown; and whether they can produce better solutions than other algorithms for certain types of graphs, and why. The introductory chapters explain graph colouring, and bounds and constructive algorithms. The author then shows how advanced, modern techniques can be applied to classic real-world operational research problems such as seating plans, sports scheduling, and university timetabling. He includes many examples, suggestions for further reading, and historical notes, and the book is supplemented by a website with an online suite of downloadable code. The book will be of value to researchers, graduate students, and practitioners in the areas of operations research, theoretical computer science, optimization, and computational intelligence. The reader should have elementary knowledge of sets, matrices, and enumerative combinatorics.
Download or read book Guide to Graph Colouring written by R. M. R. Lewis and published by Springer Nature. This book was released on 2021-10-07 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook treats graph colouring as an algorithmic problem, with a strong emphasis on practical applications. The author describes and analyses some of the best-known algorithms for colouring graphs, focusing on whether these heuristics can provide optimal solutions in some cases; how they perform on graphs where the chromatic number is unknown; and whether they can produce better solutions than other algorithms for certain types of graphs, and why. The introductory chapters explain graph colouring, complexity theory, bounds and constructive algorithms. The author then shows how advanced, graph colouring techniques can be applied to classic real-world operational research problems such as designing seating plans, sports scheduling, and university timetabling. He includes many examples, suggestions for further reading, and historical notes, and the book is supplemented by an online suite of downloadable code. The book is of value to researchers, graduate students, and practitioners in the areas of operations research, theoretical computer science, optimization, and computational intelligence. The reader should have elementary knowledge of sets, matrices, and enumerative combinatorics.
Download or read book Proceedings of the International Conference on Frontiers of Intelligent Computing Theory and Applications FICTA 2013 written by Suresh Chandra Satapathy and published by Springer Science & Business Media. This book was released on 2013-10-05 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the papers presented at the Second International Conference on Frontiers in Intelligent Computing: Theory and Applications (FICTA-2013) held during 14-16 November 2013 organized by Bhubaneswar Engineering College (BEC), Bhubaneswar, Odisha, India. It contains 63 papers focusing on application of intelligent techniques which includes evolutionary computation techniques like genetic algorithm, particle swarm optimization techniques, teaching-learning based optimization etc for various engineering applications such as data mining, Fuzzy systems, Machine Intelligence and ANN, Web technologies and Multimedia applications and Intelligent computing and Networking etc.
Download or read book Handbook of Optimization written by Ivan Zelinka and published by Springer Science & Business Media. This book was released on 2012-09-26 with total page 1088 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization problems were and still are the focus of mathematics from antiquity to the present. Since the beginning of our civilization, the human race has had to confront numerous technological challenges, such as finding the optimal solution of various problems including control technologies, power sources construction, applications in economy, mechanical engineering and energy distribution amongst others. These examples encompass both ancient as well as modern technologies like the first electrical energy distribution network in USA etc. Some of the key principles formulated in the middle ages were done by Johannes Kepler (Problem of the wine barrels), Johan Bernoulli (brachystochrone problem), Leonhard Euler (Calculus of Variations), Lagrange (Principle multipliers), that were formulated primarily in the ancient world and are of a geometric nature. In the beginning of the modern era, works of L.V. Kantorovich and G.B. Dantzig (so-called linear programming) can be considered amongst others. This book discusses a wide spectrum of optimization methods from classical to modern, alike heuristics. Novel as well as classical techniques is also discussed in this book, including its mutual intersection. Together with many interesting chapters, a reader will also encounter various methods used for proposed optimization approaches, such as game theory and evolutionary algorithms or modelling of evolutionary algorithm dynamics like complex networks.
Download or read book Graphs Colourings and the Four Colour Theorem written by Robert A. Wilson and published by OUP Oxford. This book was released on 2002-01-24 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: The four-colour theorem is one of the famous problems of mathematics, that frustrated generations of mathematicians from its birth in 1852 to its solution (using substantial assistance from electronic computers) in 1976. The theorem asks whether four colours are sufficient to colour all conceivable maps, in such a way that countries with a common border are coloured with different colours. The book discusses various attempts to solve this problem, and some of the mathematics which developed out of these attempts. Much of this mathematics has developed a life of its own, and forms a fascinating part of the subject now known as graph theory. The book is designed to be self-contained, and develops all the graph-theoretical tools needed as it goes along. It includes all the elementary graph theory that should be included in an introduction to the subject, before concentrating on specific topics relevant to the four-colour problem. Part I covers basic graph theory, Euler's polyhedral formula, and the first published false `proof' of the four-colour theorem. Part II ranges widely through related topics, including map-colouring on surfaces with holes, the famous theorems of Kuratowski, Vizing, and Brooks, the conjectures of Hadwiger and Hajos, and much more besides. In Part III we return to the four-colour theorem, and study in detail the methods which finally cracked the problem.
Download or read book Distributed Graph Coloring written by Leonid Barenboim and published by Springer Nature. This book was released on 2022-06-01 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: The focus of this monograph is on symmetry breaking problems in the message-passing model of distributed computing. In this model a communication network is represented by a n-vertex graph G = (V,E), whose vertices host autonomous processors. The processors communicate over the edges of G in discrete rounds. The goal is to devise algorithms that use as few rounds as possible. A typical symmetry-breaking problem is the problem of graph coloring. Denote by ? the maximum degree of G. While coloring G with ? + 1 colors is trivial in the centralized setting, the problem becomes much more challenging in the distributed one. One can also compromise on the number of colors, if this allows for more efficient algorithms. Other typical symmetry-breaking problems are the problems of computing a maximal independent set (MIS) and a maximal matching (MM). The study of these problems dates back to the very early days of distributed computing. The founding fathers of distributed computing laid firm foundations for the area of distributed symmetry breaking already in the eighties. In particular, they showed that all these problems can be solved in randomized logarithmic time. Also, Linial showed that an O(?2)-coloring can be solved very efficiently deterministically. However, fundamental questions were left open for decades. In particular, it is not known if the MIS or the (? + 1)-coloring can be solved in deterministic polylogarithmic time. Moreover, until recently it was not known if in deterministic polylogarithmic time one can color a graph with significantly fewer than ?2 colors. Additionally, it was open (and still open to some extent) if one can have sublogarithmic randomized algorithms for the symmetry breaking problems. Recently, significant progress was achieved in the study of these questions. More efficient deterministic and randomized (? + 1)-coloring algorithms were achieved. Deterministic ?1 + o(1)-coloring algorithms with polylogarithmic running time were devised. Improved (and often sublogarithmic-time) randomized algorithms were devised. Drastically improved lower bounds were given. Wide families of graphs in which these problems are solvable much faster than on general graphs were identified. The objective of our monograph is to cover most of these developments, and as a result to provide a treatise on theoretical foundations of distributed symmetry breaking in the message-passing model. We hope that our monograph will stimulate further progress in this exciting area.
Download or read book Introduction to Graph Theory written by Koh Khee Meng and published by World Scientific Publishing Company. This book was released on 2007-03-15 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graph theory is an area in discrete mathematics which studies configurations (called graphs) involving a set of vertices interconnected by edges. This book is intended as a general introduction to graph theory and, in particular, as a resource book for junior college students and teachers reading and teaching the subject at H3 Level in the new Singapore mathematics curriculum for junior college. The book builds on the verity that graph theory at this level is a subject that lends itself well to the development of mathematical reasoning and proof.
Download or read book Handbook of Combinatorial Optimization written by Ding-Zhu Du and published by Springer Science & Business Media. This book was released on 2006-08-18 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a supplementary volume to the major three-volume Handbook of Combinatorial Optimization set. It can also be regarded as a stand-alone volume presenting chapters dealing with various aspects of the subject in a self-contained way.
Download or read book Recent Advances in Algorithms and Combinatorics written by Bruce A. Reed and published by Springer Science & Business Media. This book was released on 2006-05-17 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excellent authors, such as Lovasz, one of the five best combinatorialists in the world; Thematic linking that makes it a coherent collection; Will appeal to a variety of communities, such as mathematics, computer science and operations research
Download or read book Graph Coloring Problems written by Tommy R. Jensen and published by John Wiley & Sons. This book was released on 2011-10-24 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains a wealth of information previously scattered in research journals, conference proceedings and technical reports. Identifies more than 200 unsolved problems. Every problem is stated in a self-contained, extremely accessible format, followed by comments on its history, related results and literature. The book will stimulate research and help avoid efforts on solving already settled problems. Each chapter concludes with a comprehensive list of references which will lead readers to original sources, important contributions and other surveys.
Download or read book Fractional Graph Theory written by Edward R. Scheinerman and published by Courier Corporation. This book was released on 2013-04-29 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume explains the general theory of hypergraphs and presents in-depth coverage of fundamental and advanced topics: fractional matching, fractional coloring, fractional edge coloring, fractional arboricity via matroid methods, fractional isomorphism, and more. 1997 edition.
Download or read book A Textbook of Graph Theory written by R. Balakrishnan and published by Springer Science & Business Media. This book was released on 2012-09-20 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: In its second edition, expanded with new chapters on domination in graphs and on the spectral properties of graphs, this book offers a solid background in the basics of graph theory. Introduces such topics as Dirac's theorem on k-connected graphs and more.
Download or read book Computational Graph Theory written by Gottfried Tinhofer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Hybrid Evolutionary Algorithms written by Crina Grosan and published by Springer. This book was released on 2007-08-29 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited volume is targeted at presenting the latest state-of-the-art methodologies in "Hybrid Evolutionary Algorithms". The chapters deal with the theoretical and methodological aspects, as well as various applications to many real world problems from science, technology, business or commerce. Overall, the book has 14 chapters including an introductory chapter giving the fundamental definitions and some important research challenges. The contributions were selected on the basis of fundamental ideas/concepts rather than the thoroughness of techniques deployed.
Download or read book The Four Color Theorem and Basic Graph Theory written by Chris McMullen and published by . This book was released on 2020-05-26 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explore a variety of fascinating concepts relating to the four-color theorem with an accessible introduction to related concepts from basic graph theory. From a clear explanation of Heawood's disproof of Kempe's argument to novel features like quadrilateral switching, this book by Chris McMullen, Ph.D., is packed with content. It even includes a novel handwaving argument explaining why the four-color theorem is true. What is the four-color theorem? Why is it common to work with graphs instead of maps? What are Kempe chains? What is the problem with Alfred Kempe's attempted proof? How does Euler's formula relate the numbers of faces, edges, and vertices? What are Kuratowski's theorem and Wagner's theorem? What is the motivation behind triangulation? What is quadrilateral switching? What is vertex splitting? What is the three-edges theorem? Is there an algorithm for four-coloring a map or graph? What is a Hamiltonian cycle? What is a separating triangle? How is the four-color theorem like an ill-conditioned logic puzzle? Why is the four-color theorem true? What makes the four-color theorem so difficult to prove by hand?
Download or read book Algorithms on Trees and Graphs written by Gabriel Valiente and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graph algorithms is a well-established subject in mathematics and computer science. Beyond classical application fields, such as approximation, combinatorial optimization, graphics, and operations research, graph algorithms have recently attracted increased attention from computational molecular biology and computational chemistry. Centered around the fundamental issue of graph isomorphism, this text goes beyond classical graph problems of shortest paths, spanning trees, flows in networks, and matchings in bipartite graphs. Advanced algorithmic results and techniques of practical relevance are presented in a coherent and consolidated way. This book introduces graph algorithms on an intuitive basis followed by a detailed exposition in a literate programming style, with correctness proofs as well as worst-case analyses. Furthermore, full C++ implementations of all algorithms presented are given using the LEDA library of efficient data structures and algorithms.
Download or read book Algorithms ESA 2007 written by Lars Arge and published by Springer. This book was released on 2007-09-17 with total page 772 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 15th Annual European Symposium on Algorithms, ESA 2007, held in Eilat, Israel, in October 2007 in the context of the combined conference ALGO 2007. The 63 revised full papers presented together with abstracts of three invited lectures address all current subjects in algorithmics reaching from design and analysis issues of algorithms over to real-world applications and engineering of algorithms in various fields.
