Graph Algorithms In The Language Of Linear Algebra

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Graph Algorithms in the Language of Linear Algebra

Jeremy Kepner,John Gilbert
Graph Algorithms in the Language of Linear Algebra Book PDF

Author : Jeremy Kepner,John Gilbert
Publisher : SIAM
Page : 388 pages
File Size : 55,5 Mb
Release : 2011-01-01
Category : Mathematics
ISBN : 0898719917

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Graph Algorithms in the Language of Linear Algebra by Jeremy Kepner,John Gilbert Pdf

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.

Graph Theory and Sparse Matrix Computation

Alan George,John R. Gilbert,Joseph W.H. Liu
Graph Theory and Sparse Matrix Computation Book PDF

Author : Alan George,John R. Gilbert,Joseph W.H. Liu
Publisher : Springer Science & Business Media
Page : 254 pages
File Size : 40,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461383697

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Graph Theory and Sparse Matrix Computation by Alan George,John R. Gilbert,Joseph W.H. Liu Pdf

When reality is modeled by computation, matrices are often the connection between the continuous physical world and the finite algorithmic one. Usually, the more detailed the model, the bigger the matrix, the better the answer, however, efficiency demands that every possible advantage be exploited. The articles in this volume are based on recent research on sparse matrix computations. This volume looks at graph theory as it connects to linear algebra, parallel computing, data structures, geometry, and both numerical and discrete algorithms. The articles are grouped into three general categories: graph models of symmetric matrices and factorizations, graph models of algorithms on nonsymmetric matrices, and parallel sparse matrix algorithms. This book will be a resource for the researcher or advanced student of either graphs or sparse matrices; it will be useful to mathematicians, numerical analysts and theoretical computer scientists alike.

Graph Algorithms in the Language of Linear Algebra

Jeremy Kepner,John Gilbert
Graph Algorithms in the Language of Linear Algebra Book PDF

Author : Jeremy Kepner,John Gilbert
Publisher : SIAM
Page : 372 pages
File Size : 46,9 Mb
Release : 2011-08-04
Category : Mathematics
ISBN : 9780898719901

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Graph Algorithms in the Language of Linear Algebra by Jeremy Kepner,John Gilbert Pdf

An introduction to graph algorithms accessible to those without a computer science background.

Graph Theory, Combinatorics and Algorithms

Martin Charles Golumbic,Irith Ben-Arroyo Hartman
Graph Theory Combinatorics and Algorithms Book PDF

Author : Martin Charles Golumbic,Irith Ben-Arroyo Hartman
Publisher : Springer Science & Business Media
Page : 296 pages
File Size : 54,8 Mb
Release : 2006-03-30
Category : Mathematics
ISBN : 9780387250366

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Graph Theory, Combinatorics and Algorithms by Martin Charles Golumbic,Irith Ben-Arroyo Hartman Pdf

Graph Theory, Combinatorics and Algorithms: Interdisciplinary Applications focuses on discrete mathematics and combinatorial algorithms interacting with real world problems in computer science, operations research, applied mathematics and engineering. The book contains eleven chapters written by experts in their respective fields, and covers a wide spectrum of high-interest problems across these discipline domains. Among the contributing authors are Richard Karp of UC Berkeley and Robert Tarjan of Princeton; both are at the pinnacle of research scholarship in Graph Theory and Combinatorics. The chapters from the contributing authors focus on "real world" applications, all of which will be of considerable interest across the areas of Operations Research, Computer Science, Applied Mathematics, and Engineering. These problems include Internet congestion control, high-speed communication networks, multi-object auctions, resource allocation, software testing, data structures, etc. In sum, this is a book focused on major, contemporary problems, written by the top research scholars in the field, using cutting-edge mathematical and computational techniques.

Graphs and Networks

S. R. Kingan
Graphs and Networks Book PDF

Author : S. R. Kingan
Publisher : John Wiley & Sons
Page : 292 pages
File Size : 53,5 Mb
Release : 2022-04-28
Category : Mathematics
ISBN : 9781118937273

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Graphs and Networks by S. R. Kingan Pdf

Graphs and Networks A unique blend of graph theory and network science for mathematicians and data science professionals alike. Featuring topics such as minors, connectomes, trees, distance, spectral graph theory, similarity, centrality, small-world networks, scale-free networks, graph algorithms, Eulerian circuits, Hamiltonian cycles, coloring, higher connectivity, planar graphs, flows, matchings, and coverings, Graphs and Networks contains modern applications for graph theorists and a host of useful theorems for network scientists. The book begins with applications to biology and the social and political sciences and gradually takes a more theoretical direction toward graph structure theory and combinatorial optimization. A background in linear algebra, probability, and statistics provides the proper frame of reference. Graphs and Networks also features: Applications to neuroscience, climate science, and the social and political sciences A research outlook integrated directly into the narrative with ideas for students interested in pursuing research projects at all levels A large selection of primary and secondary sources for further reading Historical notes that hint at the passion and excitement behind the discoveries Practice problems that reinforce the concepts and encourage further investigation and independent work

Dynamical Systems, Graphs, and Algorithms

George Osipenko
Dynamical Systems Graphs and Algorithms Book PDF

Author : George Osipenko
Publisher : Springer
Page : 288 pages
File Size : 54,7 Mb
Release : 2006-10-28
Category : Mathematics
ISBN : 9783540355953

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Dynamical Systems, Graphs, and Algorithms by George Osipenko Pdf

This book describes a family of algorithms for studying the global structure of systems. By a finite covering of the phase space we construct a directed graph with vertices corresponding to cells of the covering and edges corresponding to admissible transitions. The method is used, among other things, to locate the periodic orbits and the chain recurrent set, to construct the attractors and their basins, to estimate the entropy, and more.

Direct Methods for Sparse Linear Systems

Timothy A. Davis
Direct Methods for Sparse Linear Systems Book PDF

Author : Timothy A. Davis
Publisher : SIAM
Page : 228 pages
File Size : 43,9 Mb
Release : 2006-09-01
Category : Computers
ISBN : 9780898716139

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Direct Methods for Sparse Linear Systems by Timothy A. Davis Pdf

The sparse backslash book. Everything you wanted to know but never dared to ask about modern direct linear solvers. Chen Greif, Assistant Professor, Department of Computer Science, University of British Columbia.Overall, the book is magnificent. It fills a long-felt need for an accessible textbook on modern sparse direct methods. Its choice of scope is excellent John Gilbert, Professor, Department of Computer Science, University of California, Santa Barbara.Computational scientists often encounter problems requiring the solution of sparse systems of linear equations. Attacking these problems efficiently requires an in-depth knowledge of the underlying theory, algorithms, and data structures found in sparse matrix software libraries. Here, Davis presents the fundamentals of sparse matrix algorithms to provide the requisite background. The book includes CSparse, a concise downloadable sparse matrix package that illustrates the algorithms and theorems presented in the book and equips readers with the tools necessary to understand larger and more complex software packages.With a strong emphasis on MATLAB and the C programming language, Direct Methods for Sparse Linear Systems equips readers with the working knowledge required to use sparse solver packages and write code to interface applications to those packages. The book also explains how MATLAB performs its sparse matrix computations.Audience This invaluable book is essential to computational scientists and software developers who want to understand the theory and algorithms behind modern techniques used to solve large sparse linear systems. The book also serves as an excellent practical resource for students with an interest in combinatorial scientific computing.Preface; Chapter 1: Introduction; Chapter 2: Basic algorithms; Chapter 3: Solving triangular systems; Chapter 4: Cholesky factorization; Chapter 5: Orthogonal methods; Chapter 6: LU factorization; Chapter 7: Fill-reducing orderings; Chapter 8: Solving sparse linear systems; Chapter 9: CSparse; Chapter 10: Sparse matrices in MATLAB; Appendix: Basics of the C programming language; Bibliography; Index.

Introduction to Applied Linear Algebra

Stephen Boyd,Lieven Vandenberghe
Introduction to Applied Linear Algebra Book PDF

Author : Stephen Boyd,Lieven Vandenberghe
Publisher : Cambridge University Press
Page : 477 pages
File Size : 49,6 Mb
Release : 2018-06-07
Category : Business & Economics
ISBN : 9781316518960

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Introduction to Applied Linear Algebra by Stephen Boyd,Lieven Vandenberghe Pdf

A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.

Algorithms from THE BOOK

Kenneth Lange
Algorithms from THE BOOK Book PDF

Author : Kenneth Lange
Publisher : SIAM
Page : 227 pages
File Size : 47,7 Mb
Release : 2020-05-04
Category : Mathematics
ISBN : 9781611976175

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Algorithms from THE BOOK by Kenneth Lange Pdf

Algorithms are a dominant force in modern culture, and every indication is that they will become more pervasive, not less. The best algorithms are undergirded by beautiful mathematics. This text cuts across discipline boundaries to highlight some of the most famous and successful algorithms. Readers are exposed to the principles behind these examples and guided in assembling complex algorithms from simpler building blocks. Written in clear, instructive language within the constraints of mathematical rigor, Algorithms from THE BOOK includes a large number of classroom-tested exercises at the end of each chapter. The appendices cover background material often omitted from undergraduate courses. Most of the algorithm descriptions are accompanied by Julia code, an ideal language for scientific computing. This code is immediately available for experimentation. Algorithms from THE BOOK is aimed at first-year graduate and advanced undergraduate students. It will also serve as a convenient reference for professionals throughout the mathematical sciences, physical sciences, engineering, and the quantitative sectors of the biological and social sciences.

Thirty-three Miniatures

Jiří Matoušek
Thirty three Miniatures Book PDF

Author : Jiří Matoušek
Publisher : American Mathematical Soc.
Page : 196 pages
File Size : 42,7 Mb
Release : 2010
Category : Mathematics
ISBN : 9780821849774

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Thirty-three Miniatures by Jiří Matoušek Pdf

This volume contains a collection of clever mathematical applications of linear algebra, mainly in combinatorics, geometry, and algorithms. Each chapter covers a single main result with motivation and full proof in at most ten pages and can be read independently of all other chapters (with minor exceptions), assuming only a modest background in linear algebra. The topics include a number of well-known mathematical gems, such as Hamming codes, the matrix-tree theorem, the Lovasz bound on the Shannon capacity, and a counterexample to Borsuk's conjecture, as well as other, perhaps less popular but similarly beautiful results, e.g., fast associativity testing, a lemma of Steinitz on ordering vectors, a monotonicity result for integer partitions, or a bound for set pairs via exterior products. The simpler results in the first part of the book provide ample material to liven up an undergraduate course of linear algebra. The more advanced parts can be used for a graduate course of linear-algebraic methods or for seminar presentations. Table of Contents: Fibonacci numbers, quickly; Fibonacci numbers, the formula; The clubs of Oddtown; Same-size intersections; Error-correcting codes; Odd distances; Are these distances Euclidean?; Packing complete bipartite graphs; Equiangular lines; Where is the triangle?; Checking matrix multiplication; Tiling a rectangle by squares; Three Petersens are not enough; Petersen, Hoffman-Singleton, and maybe 57; Only two distances; Covering a cube minus one vertex; Medium-size intersection is hard to avoid; On the difficulty of reducing the diameter; The end of the small coins; Walking in the yard; Counting spanning trees; In how many ways can a man tile a board?; More bricks--more walls?; Perfect matchings and determinants; Turning a ladder over a finite field; Counting compositions; Is it associative?; The secret agent and umbrella; Shannon capacity of the union: a tale of two fields; Equilateral sets; Cutting cheaply using eigenvectors; Rotating the cube; Set pairs and exterior products; Index. (STML/53)

Algorithmic Mathematics

Stefan Hougardy,Jens Vygen
Algorithmic Mathematics Book PDF

Author : Stefan Hougardy,Jens Vygen
Publisher : Springer
Page : 163 pages
File Size : 44,8 Mb
Release : 2016-10-14
Category : Computers
ISBN : 9783319395586

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Algorithmic Mathematics by Stefan Hougardy,Jens Vygen Pdf

Algorithms play an increasingly important role in nearly all fields of mathematics. This book allows readers to develop basic mathematical abilities, in particular those concerning the design and analysis of algorithms as well as their implementation. It presents not only fundamental algorithms like the sieve of Eratosthenes, the Euclidean algorithm, sorting algorithms, algorithms on graphs, and Gaussian elimination, but also discusses elementary data structures, basic graph theory, and numerical questions. In addition, it provides an introduction to programming and demonstrates in detail how to implement algorithms in C++. This textbook is suitable for students who are new to the subject and covers a basic mathematical lecture course, complementing traditional courses on analysis and linear algebra. Both authors have given this "Algorithmic Mathematics" course at the University of Bonn several times in recent years.

Algebraic Graph Algorithms

K. Erciyes
Algebraic Graph Algorithms Book PDF

Author : K. Erciyes
Publisher : Springer Nature
Page : 229 pages
File Size : 41,9 Mb
Release : 2021-11-17
Category : Computers
ISBN : 9783030878863

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Algebraic Graph Algorithms by K. Erciyes Pdf

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.

Graphs and Matrices

Ravindra B. Bapat
Graphs and Matrices Book PDF

Author : Ravindra B. Bapat
Publisher : Springer
Page : 193 pages
File Size : 51,8 Mb
Release : 2014-09-19
Category : Mathematics
ISBN : 9781447165699

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Graphs and Matrices by Ravindra B. Bapat Pdf

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.

Graph Algorithms

Mark Needham,Amy E. Hodler
Graph Algorithms Book PDF

Author : Mark Needham,Amy E. Hodler
Publisher : "O'Reilly Media, Inc."
Page : 297 pages
File Size : 46,9 Mb
Release : 2019-05-16
Category : Computers
ISBN : 9781492047636

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Graph Algorithms by Mark Needham,Amy E. Hodler Pdf

Discover how graph algorithms can help you leverage the relationships within your data to develop more intelligent solutions and enhance your machine learning models. You’ll learn how graph analytics are uniquely suited to unfold complex structures and reveal difficult-to-find patterns lurking in your data. Whether you are trying to build dynamic network models or forecast real-world behavior, this book illustrates how graph algorithms deliver value—from finding vulnerabilities and bottlenecks to detecting communities and improving machine learning predictions. This practical book walks you through hands-on examples of how to use graph algorithms in Apache Spark and Neo4j—two of the most common choices for graph analytics. Also included: sample code and tips for over 20 practical graph algorithms that cover optimal pathfinding, importance through centrality, and community detection. Learn how graph analytics vary from conventional statistical analysis Understand how classic graph algorithms work, and how they are applied Get guidance on which algorithms to use for different types of questions Explore algorithm examples with working code and sample datasets from Spark and Neo4j See how connected feature extraction can increase machine learning accuracy and precision Walk through creating an ML workflow for link prediction combining Neo4j and Spark

Max-linear Systems: Theory and Algorithms

Peter Butkovič
Max linear Systems Theory and Algorithms Book PDF

Author : Peter Butkovič
Publisher : Springer Science & Business Media
Page : 274 pages
File Size : 45,6 Mb
Release : 2010-08-05
Category : Mathematics
ISBN : 9781849962995

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Max-linear Systems: Theory and Algorithms by Peter Butkovič Pdf

Recent years have seen a significant rise of interest in max-linear theory and techniques. Specialised international conferences and seminars or special sessions devoted to max-algebra have been organised. This book aims to provide a first detailed and self-contained account of linear-algebraic aspects of max-algebra for general (that is both irreducible and reducible) matrices. Among the main features of the book is the presentation of the fundamental max-algebraic theory (Chapters 1-4), often scattered in research articles, reports and theses, in one place in a comprehensive and unified form. This presentation is made with all proofs and in full generality (that is for both irreducible and reducible matrices). Another feature is the presence of advanced material (Chapters 5-10), most of which has not appeared in a book before and in many cases has not been published at all. Intended for a wide-ranging readership, this book will be useful for anyone with basic mathematical knowledge (including undergraduate students) who wish to learn fundamental max-algebraic ideas and techniques. It will also be useful for researchers working in tropical geometry or idempotent analysis.