Algebraic Graph Algorithms
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| Author | : K. Erciyes |
| Publisher | : Springer Nature |
| Total Pages | : 229 |
| Release | : 2021-11-17 |
| Genre | : Computers |
| ISBN | : 3030878864 |
This textbook discusses the design and implementation of basic algebraic graph algorithms, and algebraic graph algorithms for complex networks, employing matroids whenever possible. The text describes the design of a simple parallel matrix algorithm kernel that can be used for parallel processing of algebraic graph algorithms. Example code is presented in pseudocode, together with case studies in Python and MPI. The text assumes readers have a background in graph theory and/or graph algorithms.
| Author | : Jeremy Kepner |
| Publisher | : SIAM |
| Total Pages | : 388 |
| Release | : 2011-01-01 |
| Genre | : Mathematics |
| ISBN | : 9780898719918 |
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.
| Author | : Chris Godsil |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 453 |
| Release | : 2013-12-01 |
| Genre | : Mathematics |
| ISBN | : 1461301637 |
This book presents and illustrates the main tools and ideas of algebraic graph theory, with a primary emphasis on current rather than classical topics. It is designed to offer self-contained treatment of the topic, with strong emphasis on concrete examples.
| Author | : K Erciyes |
| Publisher | : Springer |
| Total Pages | : 475 |
| Release | : 2018-04-13 |
| Genre | : Computers |
| ISBN | : 3319732358 |
This clearly structured textbook/reference presents a detailed and comprehensive review of the fundamental principles of sequential graph algorithms, approaches for NP-hard graph problems, and approximation algorithms and heuristics for such problems. The work also provides a comparative analysis of sequential, parallel and distributed graph algorithms – including algorithms for big data – and an investigation into the conversion principles between the three algorithmic methods. Topics and features: presents a comprehensive analysis of sequential graph algorithms; offers a unifying view by examining the same graph problem from each of the three paradigms of sequential, parallel and distributed algorithms; describes methods for the conversion between sequential, parallel and distributed graph algorithms; surveys methods for the analysis of large graphs and complex network applications; includes full implementation details for the problems presented throughout the text; provides additional supporting material at an accompanying website. This practical guide to the design and analysis of graph algorithms is ideal for advanced and graduate students of computer science, electrical and electronic engineering, and bioinformatics. The material covered will also be of value to any researcher familiar with the basics of discrete mathematics, graph theory and algorithms.
| Author | : Sriraman Sridharan |
| Publisher | : CRC Press |
| Total Pages | : 320 |
| Release | : 2019-07-30 |
| Genre | : Mathematics |
| ISBN | : 0429942621 |
Conveying ideas in a user-friendly style, this book has been designed for a course in Applied Algebra. The book covers graph algorithms, basic algebraic structures, coding theory and cryptography. It will be most suited for senior undergraduates and beginning graduate students in mathematics and computer science as also to individuals who want to have a knowledge of the below-mentioned topics. Provides a complete discussion on several graph algorithms such as Prims algorithm and Kruskals algorithm for sending a minimum cost spanning tree in a weighted graph, Dijkstras single source shortest path algorithm, Floyds algorithm, Warshalls algorithm, Kuhn-Munkres Algorithm. In addition to DFS and BFS search, several applications of DFS and BFS are also discussed. Presents a good introduction to the basic algebraic structures, namely, matrices, groups, rings, fields including finite fields as also a discussion on vector spaces and linear equations and their solutions. Provides an introduction to linear codes including cyclic codes. Presents a description of private key cryptosystems as also a discussion on public key cryptosystems such as RSA, ElGamal and Miller-Rabin. Finally, the Agrawal-KayalSaxena algorithm (AKS Algorithm) for testing if a given positive integer is prime or not in polynomial time is presented- the first time in a textbook. Two distinguished features of the book are: Illustrative examples have been presented throughout the book to make the readers appreciate the concepts described. Answers to all even-numbered exercises in all the chapters are given.
| Author | : Sriraman Sridharan |
| Publisher | : CRC Press |
| Total Pages | : 314 |
| Release | : 2019-07-30 |
| Genre | : Mathematics |
| ISBN | : 042994263X |
Conveying ideas in a user-friendly style, this book has been designed for a course in Applied Algebra. The book covers graph algorithms, basic algebraic structures, coding theory and cryptography. It will be most suited for senior undergraduates and beginning graduate students in mathematics and computer science as also to individuals who want to have a knowledge of the below-mentioned topics. Provides a complete discussion on several graph algorithms such as Prims algorithm and Kruskals algorithm for sending a minimum cost spanning tree in a weighted graph, Dijkstras single source shortest path algorithm, Floyds algorithm, Warshalls algorithm, Kuhn-Munkres Algorithm. In addition to DFS and BFS search, several applications of DFS and BFS are also discussed. Presents a good introduction to the basic algebraic structures, namely, matrices, groups, rings, fields including finite fields as also a discussion on vector spaces and linear equations and their solutions. Provides an introduction to linear codes including cyclic codes. Presents a description of private key cryptosystems as also a discussion on public key cryptosystems such as RSA, ElGamal and Miller-Rabin. Finally, the Agrawal-KayalSaxena algorithm (AKS Algorithm) for testing if a given positive integer is prime or not in polynomial time is presented- the first time in a textbook. Two distinguished features of the book are: Illustrative examples have been presented throughout the book to make the readers appreciate the concepts described. Answers to all even-numbered exercises in all the chapters are given.
| Author | : Ton Kloks |
| Publisher | : Springer Nature |
| Total Pages | : 340 |
| Release | : 2022-02-22 |
| Genre | : Computers |
| ISBN | : 9811663505 |
This book A Guide to Graph Algorithms offers high-quality content in the research area of graph algorithms and explores the latest developments in graph algorithmics. The reader will gain a comprehensive understanding of how to use algorithms to explore graphs. It is a collection of texts that have proved to be trend setters and good examples of that. The book aims at providing the reader with a deep understanding of the structural properties of graphs that are useful for the design of efficient algorithms. These algorithms have applications in finite state machine modelling, social network theory, biology, and mathematics. The book contains many exercises, some up at present-day research-level. The exercises encourage the reader to discover new techniques by putting things in a clear perspective. A study of this book will provide the reader with many powerful tools to model and tackle problems in real-world scenarios.
| Author | : Piotr Sankowski |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2005 |
| Genre | : |
| ISBN | : |
Dotyczy: dynamic slgorithms, determinant, matrixinverse, adjoint, transitive closure, shortest paths, perfect matchings, spanning trees .
| Author | : Lowell W. Beineke |
| Publisher | : Cambridge University Press |
| Total Pages | : 302 |
| Release | : 2004-10-04 |
| Genre | : Mathematics |
| ISBN | : 9780521801973 |
There is no other book with such a wide scope of both areas of algebraic graph theory.
| Author | : Ravindra B. Bapat |
| Publisher | : Springer |
| Total Pages | : 197 |
| Release | : 2014-09-19 |
| Genre | : Mathematics |
| ISBN | : 1447165691 |
This new edition illustrates the power of linear algebra in the study of graphs. The emphasis on matrix techniques is greater than in other texts on algebraic graph theory. Important matrices associated with graphs (for example, incidence, adjacency and Laplacian matrices) are treated in detail. Presenting a useful overview of selected topics in algebraic graph theory, early chapters of the text focus on regular graphs, algebraic connectivity, the distance matrix of a tree, and its generalized version for arbitrary graphs, known as the resistance matrix. Coverage of later topics include Laplacian eigenvalues of threshold graphs, the positive definite completion problem and matrix games based on a graph. Such an extensive coverage of the subject area provides a welcome prompt for further exploration. The inclusion of exercises enables practical learning throughout the book. In the new edition, a new chapter is added on the line graph of a tree, while some results in Chapter 6 on Perron-Frobenius theory are reorganized. Whilst this book will be invaluable to students and researchers in graph theory and combinatorial matrix theory, it will also benefit readers in the sciences and engineering.
