Optimization Problems In Graph Theory

Author : Boris Goldengorin
Publisher : Springer
Page : 331 pages
File Size : 43,8 Mb
Release : 2018-09-27
Category : Mathematics
ISBN : 9783319948300

Get Book

Optimization Problems in Graph Theory by Boris Goldengorin Pdf

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

Author : David Avis,Alain Hertz,Odile Marcotte
Publisher : Springer Science & Business Media
Page : 286 pages
File Size : 55,7 Mb
Release : 2005-04-28
Category : Business & Economics
ISBN : 0387255915

Get Book

Graph Theory and Combinatorial Optimization by David Avis,Alain Hertz,Odile Marcotte Pdf

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.

Author : William Kocay,Donald L. Kreher
Publisher : CRC Press
Page : 504 pages
File Size : 53,8 Mb
Release : 2017-09-20
Category : Mathematics
ISBN : 9781351989121

Get Book

Graphs, Algorithms, and Optimization by William Kocay,Donald L. Kreher Pdf

Graph theory offers a rich source of problems and techniques for programming and data structure development, as well as for understanding computing theory, including NP-Completeness and polynomial reduction. A comprehensive text, Graphs, Algorithms, and Optimization features clear exposition on modern algorithmic graph theory presented in a rigorous yet approachable way. The book covers major areas of graph theory including discrete optimization and its connection to graph algorithms. The authors explore surface topology from an intuitive point of view and include detailed discussions on linear programming that emphasize graph theory problems useful in mathematics and computer science. Many algorithms are provided along with the data structure needed to program the algorithms efficiently. The book also provides coverage on algorithm complexity and efficiency, NP-completeness, linear optimization, and linear programming and its relationship to graph algorithms. Written in an accessible and informal style, this work covers nearly all areas of graph theory. Graphs, Algorithms, and Optimization provides a modern discussion of graph theory applicable to mathematics, computer science, and crossover applications.

Author : Krishnaiyan "KT" Thulasiraman,Subramanian Arumugam,Andreas Brandstädt,Takao Nishizeki
Publisher : CRC Press
Page : 1217 pages
File Size : 45,9 Mb
Release : 2016-01-05
Category : Computers
ISBN : 9781420011074

Get Book

Handbook of Graph Theory, Combinatorial Optimization, and Algorithms by Krishnaiyan "KT" Thulasiraman,Subramanian Arumugam,Andreas Brandstädt,Takao Nishizeki Pdf

The fusion between graph theory and combinatorial optimization has led to theoretically profound and practically useful algorithms, yet there is no book that currently covers both areas together. Handbook of Graph Theory, Combinatorial Optimization, and Algorithms is the first to present a unified, comprehensive treatment of both graph theory and c

Author : Hang T. Lau
Publisher : CRC Press
Page : 401 pages
File Size : 53,5 Mb
Release : 2006-10-20
Category : Computers
ISBN : 9781584887195

Get Book

A Java Library of Graph Algorithms and Optimization by Hang T. Lau Pdf

Because of its portability and platform-independence, Java is the ideal computer programming language to use when working on graph algorithms and other mathematical programming problems. Collecting some of the most popular graph algorithms and optimization procedures, A Java Library of Graph Algorithms and Optimization provides the source code for

Author : Saoussen Krichen,Jouhaina Chaouachi
Publisher : John Wiley & Sons
Page : 175 pages
File Size : 54,6 Mb
Release : 2014-10-06
Category : Computers
ISBN : 9781848217430

Get Book

Graph-related Optimization and Decision Support Systems by Saoussen Krichen,Jouhaina Chaouachi Pdf

Constrained optimization is a challenging branch of operations research that aims to create a model which has a wide range of applications in the supply chain, telecommunications and medical fields. As the problem structure is split into two main components, the objective is to accomplish the feasible set framed by the system constraints. The aim of this book is expose optimization problems that can be expressed as graphs, by detailing, for each studied problem, the set of nodes and the set of edges. This graph modeling is an incentive for designing a platform that integrates all optimization components in order to output the best solution regarding the parameters' tuning. The authors propose in their analysis, for optimization problems, to provide their graphical modeling and mathematical formulation and expose some of their variants. As a solution approaches, an optimizer can be the most promising direction for limited-size instances. For large problem instances, approximate algorithms are the most appropriate way for generating high quality solutions. The authors thus propose, for each studied problem, a greedy algorithm as a problem-specific heuristic and a genetic algorithm as a metaheuristic.

Author : William Kocay,Donald L. Kreher
Publisher : CRC Press
Page : 566 pages
File Size : 45,6 Mb
Release : 2016-11-03
Category : Mathematics
ISBN : 9781482251180

Get Book

Graphs, Algorithms, and Optimization by William Kocay,Donald L. Kreher Pdf

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.

Author : Bernhard Korte,Jens Vygen
Publisher : Springer Science & Business Media
Page : 596 pages
File Size : 45,5 Mb
Release : 2006-01-27
Category : Mathematics
ISBN : 9783540292975

Get Book

Combinatorial Optimization by Bernhard Korte,Jens Vygen Pdf

This well-written textbook on combinatorial optimization puts special emphasis on theoretical results and algorithms with provably good performance, in contrast to heuristics. The book contains complete (but concise) proofs, as well as many deep results, some of which have not appeared in any previous books.

Author : Ken Levasseur,Al Doerr
Publisher : Lulu.com
Page : 574 pages
File Size : 55,7 Mb
Release : 2012-02-25
Category : Applied mathematics
ISBN : 9781105559297

Get Book

Applied Discrete Structures by Ken Levasseur,Al Doerr Pdf

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.

Author : Christopher H Griffin
Publisher : World Scientific
Page : 305 pages
File Size : 46,7 Mb
Release : 2023-08-08
Category : Mathematics
ISBN : 9789811273124

Get Book

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

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.

Author : E. Boros,P.L. Hammer
Publisher : Elsevier
Page : 587 pages
File Size : 50,7 Mb
Release : 2003-03-19
Category : Mathematics
ISBN : 9780080930282

Get Book

Discrete Optimization by E. Boros,P.L. Hammer Pdf

One of the most frequently occurring types of optimization problems involves decision variables which have to take integer values. From a practical point of view, such problems occur in countless areas of management, engineering, administration, etc., and include such problems as location of plants or warehouses, scheduling of aircraft, cutting raw materials to prescribed dimensions, design of computer chips, increasing reliability or capacity of networks, etc. This is the class of problems known in the professional literature as "discrete optimization" problems. While these problems are of enormous applicability, they present many challenges from a computational point of view. This volume is an update on the impressive progress achieved by mathematicians, operations researchers, and computer scientists in solving discrete optimization problems of very large sizes. The surveys in this volume present a comprehensive overview of the state of the art in discrete optimization and are written by the most prominent researchers from all over the world. This volume describes the tremendous progress in discrete optimization achieved in the last 20 years since the publication of Discrete Optimization '77, Annals of Discrete Mathematics, volumes 4 and 5, 1979 (Elsevier). It contains surveys of the state of the art written by the most prominent researchers in the field from all over the world, and covers topics like neighborhood search techniques, lift and project for mixed 0-1 programming, pseudo-Boolean optimization, scheduling and assignment problems, production planning, location, bin packing, cutting planes, vehicle routing, and applications to graph theory, mechanics, chip design, etc. Key features: • state of the art surveys • comprehensiveness • prominent authors • theoretical, computational and applied aspects. This book is a reprint of Discrete Applied Mathematics Volume 23, Numbers 1-3

Author : G. Ausiello,M. Lucertini
Publisher : Elsevier
Page : 318 pages
File Size : 51,6 Mb
Release : 1985-05-01
Category : Mathematics
ISBN : 0080872204

Get Book

Analysis and Design of Algorithms for Combinatorial Problems by G. Ausiello,M. Lucertini Pdf

Combinatorial problems have been from the very beginning part of the history of mathematics. By the Sixties, the main classes of combinatorial problems had been defined. During that decade, a great number of research contributions in graph theory had been produced, which laid the foundations for most of the research in graph optimization in the following years. During the Seventies, a large number of special purpose models were developed. The impressive growth of this field since has been strongly determined by the demand of applications and influenced by the technological increases in computing power and the availability of data and software. The availability of such basic tools has led to the feasibility of the exact or well approximate solution of large scale realistic combinatorial optimization problems and has created a number of new combinatorial problems.

Author : Cécile Murat,Vangelis Th. Paschos
Publisher : John Wiley & Sons
Page : 202 pages
File Size : 43,9 Mb
Release : 2013-03-01
Category : Mathematics
ISBN : 9781118614136

Get Book

Probabilistic Combinatorial Optimization on Graphs by Cécile Murat,Vangelis Th. Paschos Pdf

This title provides a comprehensive survey over the subject of probabilistic combinatorial optimization, discussing probabilistic versions of some of the most paradigmatic combinatorial problems on graphs, such as the maximum independent set, the minimum vertex covering, the longest path and the minimum coloring. Those who possess a sound knowledge of the subject mater will find the title of great interest, but those who have only some mathematical familiarity and knowledge about complexity and approximation theory will also find it an accessible and informative read.

Author : Y. Alavi,Allen Schwenk
Publisher : Unknown
Page : 426 pages
File Size : 44,8 Mb
Release : 1995
Category : Algorithms
ISBN : UOM:39015035021636

Get Book

Graph Theory, Combinatorics, and Algorithms by Y. Alavi,Allen Schwenk Pdf

Author : Takuro Fukunaga,Ken-ichi Kawarabayashi
Publisher : Springer
Page : 120 pages
File Size : 52,7 Mb
Release : 2017-10-02
Category : Computers
ISBN : 9789811061479

Get Book

Combinatorial Optimization and Graph Algorithms by Takuro Fukunaga,Ken-ichi Kawarabayashi Pdf

Covering network designs, discrete convex analysis, facility location and clustering problems, matching games, and parameterized complexity, this book discusses theoretical aspects of combinatorial optimization and graph algorithms. Contributions are by renowned researchers who attended NII Shonan meetings on this essential topic. The collection contained here provides readers with the outcome of the authors’ research and productive meetings on this dynamic area, ranging from computer science and mathematics to operations research. Networks are ubiquitous in today's world: the Web, online social networks, and search-and-query click logs can lead to a graph that consists of vertices and edges. Such networks are growing so fast that it is essential to design algorithms to work for these large networks. Graph algorithms comprise an area in computer science that works to design efficient algorithms for networks. Here one can work on theoretical or practical problems where implementation of an algorithm for large networks is needed. In two of the chapters, recent results in graph matching games and fixed parameter tractability are surveyed. Combinatorial optimization is an intersection of operations research and mathematics, especially discrete mathematics, which deals with new questions and new problems, attempting to find an optimum object from a finite set of objects. Most problems in combinatorial optimization are not tractable (i.e., NP-hard). Therefore it is necessary to design an approximation algorithm for them. To tackle these problems requires the development and combination of ideas and techniques from diverse mathematical areas including complexity theory, algorithm theory, and matroids as well as graph theory, combinatorics, convex and nonlinear optimization, and discrete and convex geometry. Overall, the book presents recent progress in facility location, network design, and discrete convex analysis.