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Optimization Problems in Graph Theory

2018-09-27 Mathematics
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Release : 2018-09-27
Genre : Mathematics
Kind : eBook
Book Rating : 30X/5 ( reviews)

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Book Synopsis Optimization Problems in Graph Theory by : Boris Goldengorin

Download or read book Optimization Problems in Graph Theory written by Boris Goldengorin. This book was released on 2018-09-27. Available in PDF, EPUB and Kindle. Book excerpt: This book presents open optimization problems in graph theory and networks. Each chapter reflects developments in theory and applications based on Gregory Gutin’s fundamental contributions to advanced methods and techniques in combinatorial optimization. Researchers, students, and engineers in computer science, big data, applied mathematics, operations research, algorithm design, artificial intelligence, software engineering, data analysis, industrial and systems engineering will benefit from the state-of-the-art results presented in modern graph theory and its applications to the design of efficient algorithms for optimization problems. Topics covered in this work include: · Algorithmic aspects of problems with disjoint cycles in graphs · Graphs where maximal cliques and stable sets intersect · The maximum independent set problem with special classes · A general technique for heuristic algorithms for optimization problems · The network design problem with cut constraints · Algorithms for computing the frustration index of a signed graph · A heuristic approach for studying the patrol problem on a graph · Minimum possible sum and product of the proper connection number · Structural and algorithmic results on branchings in digraphs · Improved upper bounds for Korkel--Ghosh benchmark SPLP instances

Graph Theory and Combinatorial Optimization

2005-04-28 Business & Economics
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Release : 2005-04-28
Genre : Business & Economics
Kind : eBook
Book Rating : 910/5 ( reviews)

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Book Synopsis Graph Theory and Combinatorial Optimization by : David Avis

Download or read book Graph Theory and Combinatorial Optimization written by David Avis. This book was released on 2005-04-28. Available in PDF, EPUB and Kindle. Book excerpt: Graph theory is very much tied to the geometric properties of optimization and combinatorial optimization. Moreover, graph theory's geometric properties are at the core of many research interests in operations research and applied mathematics. Its techniques have been used in solving many classical problems including maximum flow problems, independent set problems, and the traveling salesman problem. Graph Theory and Combinatorial Optimization explores the field's classical foundations and its developing theories, ideas and applications to new problems. The book examines the geometric properties of graph theory and its widening uses in combinatorial optimization theory and application. The field's leading researchers have contributed chapters in their areas of expertise.

Applied Graph Theory: An Introduction With Graph Optimization And Algebraic Graph Theory

2023-08-08 Mathematics
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Release : 2023-08-08
Genre : Mathematics
Kind : eBook
Book Rating : 12X/5 ( reviews)

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Book Synopsis Applied Graph Theory: An Introduction With Graph Optimization And Algebraic Graph Theory by : Christopher H Griffin

Download or read book Applied Graph Theory: An Introduction With Graph Optimization And Algebraic Graph Theory written by Christopher H Griffin. This book was released on 2023-08-08. Available in PDF, EPUB and Kindle. Book excerpt: This book serves as an introduction to graph theory and its applications. It is intended for a senior undergraduate course in graph theory but is also appropriate for beginning graduate students in science or engineering. The book presents a rigorous (proof-based) introduction to graph theory while also discussing applications of the results for solving real-world problems of interest. The book is divided into four parts. Part 1 covers the combinatorial aspects of graph theory including a discussion of common vocabulary, a discussion of vertex and edge cuts, Eulerian tours, Hamiltonian paths and a characterization of trees. This leads to Part 2, which discusses common combinatorial optimization problems. Spanning trees, shortest path problems and matroids are all discussed, as are maximum flow problems. Part 2 ends with a discussion of graph coloring and a proof of the NP-completeness of the coloring problem. Part 3 introduces the reader to algebraic graph theory, and focuses on Markov chains, centrality computation (e.g., eigenvector centrality and page rank), as well as spectral graph clustering and the graph Laplacian. Part 4 contains additional material on linear programming, which is used to provide an alternative analysis of the maximum flow problem. Two appendices containing prerequisite material on linear algebra and probability theory are also provided.

Graphs, Algorithms, and Optimization, Second Edition

2016-11-03 Mathematics
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Release : 2016-11-03
Genre : Mathematics
Kind : eBook
Book Rating : 256/5 ( reviews)

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Book Synopsis Graphs, Algorithms, and Optimization, Second Edition by : William Kocay

Download or read book Graphs, Algorithms, and Optimization, Second Edition written by William Kocay. This book was released on 2016-11-03. Available in PDF, EPUB and Kindle. Book excerpt: The second edition of this popular book presents the theory of graphs from an algorithmic viewpoint. The authors present the graph theory in a rigorous, but informal style and cover most of the main areas of graph theory. The ideas of surface topology are presented from an intuitive point of view. We have also included a discussion on linear programming that emphasizes problems in graph theory. The text is suitable for students in computer science or mathematics programs. ?

Applied Discrete Structures

2012-02-25 Applied mathematics
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Release : 2012-02-25
Genre : Applied mathematics
Kind : eBook
Book Rating : 297/5 ( reviews)

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Book Synopsis Applied Discrete Structures by : Ken Levasseur

Download or read book Applied Discrete Structures written by Ken Levasseur. This book was released on 2012-02-25. Available in PDF, EPUB and Kindle. Book excerpt: Applied Discrete Structures, is a two semester undergraduate text in discrete mathematics, focusing on the structural properties of mathematical objects. These include matrices, functions, graphs, trees, lattices and algebraic structures. The algebraic structures that are discussed are monoids, groups, rings, fields and vector spaces. Website: http: //discretemath.org Applied Discrete Structures has been approved by the American Institute of Mathematics as part of their Open Textbook Initiative. For more information on open textbooks, visit http: //www.aimath.org/textbooks/. This version was created using Mathbook XML (https: //mathbook.pugetsound.edu/) Al Doerr is Emeritus Professor of Mathematical Sciences at UMass Lowell. His interests include abstract algebra and discrete mathematics. Ken Levasseur is a Professor of Mathematical Sciences at UMass Lowell. His interests include discrete mathematics and abstract algebra, and their implementation using computer algebra systems.

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