Matroid Applications

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Matroid Applications

Author : Neil White
Publisher : Cambridge University Press
Page : 377 pages
File Size : 47,5 Mb
Release : 1992-03-05
Category : Mathematics
ISBN : 9780521381659

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Matroid Applications by Neil White Pdf

This volume, the third in a sequence that began with The Theory of Matroids and Combinatorial Geometries, concentrates on the applications of matroid theory to a variety of topics from engineering (rigidity and scene analysis), combinatorics (graphs, lattices, codes and designs), topology and operations research (the greedy algorithm).

Matroid Theory and its Applications in Electric Network Theory and in Statics

Author : Andras Recski
Publisher : Springer Science & Business Media
Page : 542 pages
File Size : 55,9 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783662221433

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Matroid Theory and its Applications in Electric Network Theory and in Statics by Andras Recski Pdf

I. The topics of this book The concept of a matroid has been known for more than five decades. Whitney (1935) introduced it as a common generalization of graphs and matrices. In the last two decades, it has become clear how important the concept is, for the following reasons: (1) Combinatorics (or discrete mathematics) was considered by many to be a collection of interesting, sometimes deep, but mostly unrelated ideas. However, like other branches of mathematics, combinatorics also encompasses some gen eral tools that can be learned and then applied, to various problems. Matroid theory is one of these tools. (2) Within combinatorics, the relative importance of algorithms has in creased with the spread of computers. Classical analysis did not even consider problems where "only" a finite number of cases were to be studied. Now such problems are not only considered, but their complexity is often analyzed in con siderable detail. Some questions of this type (for example, the determination of when the so called "greedy" algorithm is optimal) cannot even be answered without matroidal tools.

Theory of Matroids

Author : Neil White
Publisher : Cambridge University Press
Page : 341 pages
File Size : 52,7 Mb
Release : 1986-04-03
Category : Mathematics
ISBN : 9780521309370

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Theory of Matroids by Neil White Pdf

The theory of matroids is unique in the extent to which it connects such disparate branches of combinatorial theory and algebra as graph theory, lattice theory, design theory, combinatorial optimization, linear algebra, group theory, ring theory and field theory. Furthermore, matroid theory is alone among mathematical theories because of the number and variety of its equivalent axiom systems. Indeed, matroids are amazingly versatile and the approaches to the subject are varied and numerous. This book is a primer in the basic axioms and constructions of matroids. The contributions by various leaders in the field include chapters on axiom systems, lattices, basis exchange properties, orthogonality, graphs and networks, constructions, maps, semi-modular functions and an appendix on cryptomorphisms. The authors have concentrated on giving a lucid exposition of the individual topics; explanations of theorems are preferred to complete proofs and original work is thoroughly referenced. In addition, exercises are included for each topic.

Oriented Matroids

Author : Anders Björner
Publisher : Cambridge University Press
Page : 564 pages
File Size : 50,5 Mb
Release : 1999-11-18
Category : Mathematics
ISBN : 9780521777506

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Oriented Matroids by Anders Björner Pdf

First comprehensive, accessible account; second edition has expanded bibliography and a new appendix surveying recent research.

Matroids: A Geometric Introduction

Author : Gary Gordon,Jennifer McNulty
Publisher : Cambridge University Press
Page : 411 pages
File Size : 47,8 Mb
Release : 2012-08-02
Category : Language Arts & Disciplines
ISBN : 9780521145688

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Matroids: A Geometric Introduction by Gary Gordon,Jennifer McNulty Pdf

This friendly introduction helps undergraduate students understand and appreciate matroid theory and its connections to geometry.

Matrices and Matroids for Systems Analysis

Author : Kazuo Murota
Publisher : Springer Science & Business Media
Page : 500 pages
File Size : 55,6 Mb
Release : 1999-11-29
Category : Mathematics
ISBN : 3540660240

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Matrices and Matroids for Systems Analysis by Kazuo Murota Pdf

A matroid is an abstract mathematical structure that captures combinatorial properties of matrices. This book offers a unique introduction to matroid theory, emphasizing motivations from matrix theory and applications to systems analysis. This book serves also as a comprehensive presentation of the theory and application of mixed matrices, developed primarily by the present author in the 1990's. A mixed matrix is a convenient mathematical tool for systems analysis, compatible with the physical observation that "fixed constants" and "system parameters" are to be distinguished in the description of engineering systems. This book will be extremely useful to graduate students and researchers in engineering, mathematics and computer science. From the reviews: "...The book has been prepared very carefully, contains a lot of interesting results and is highly recommended for graduate and postgraduate students." András Recski, Mathematical Reviews Clippings 2000m:93006

Matroid Applications

Author : Neil White
Publisher : Unknown
Page : 376 pages
File Size : 52,9 Mb
Release : 1992
Category : Electronic books
ISBN : 1107094267

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Matroid Applications by Neil White Pdf

This volume deals with the applications of matroid theory to a variety of topics.

Matroid Theory

Author : Joseph Edmond Bonin
Publisher : American Mathematical Soc.
Page : 418 pages
File Size : 54,5 Mb
Release : 1996
Category : Mathematics
ISBN : 9780821805084

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Matroid Theory by Joseph Edmond Bonin Pdf

This volume contains the proceedings of the 1995 AMS-IMS-SIAM Joint Summer Research Conference on Matroid Theory held at the University of Washington, Seattle. The book features three comprehensive surveys that bring the reader to the forefront of research in matroid theory. Joseph Kung's encyclopedic treatment of the critical problem traces the development of this problem from its origins through its numerous links with other branches of mathematics to the current status of its many aspects. James Oxley's survey of the role of connectivity and structure theorems in matroid theory stresses the influence of the Wheels and Whirls Theorem of Tutte and the Splitter Theorem of Seymour. Walter Whiteley's article unifies applications of matroid theory to constrained geometrical systems, including the rigidity of bar-and-joint frameworks, parallel drawings, and splines. These widely accessible articles contain many new results and directions for further research and applications. The surveys are complemented by selected short research papers. The volume concludes with a chapter of open problems. Features self-contained, accessible surveys of three active research areas in matroid theory; many new results; pointers to new research topics; a chapter of open problems; mathematical applications; and applications and connections to other disciplines, such as computer-aided design and electrical and structural engineering.

Matroids: A Geometric Introduction

Author : Gary Gordon,Jennifer McNulty
Publisher : Cambridge University Press
Page : 128 pages
File Size : 44,6 Mb
Release : 2012-08-02
Category : Mathematics
ISBN : 9781139536080

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Matroids: A Geometric Introduction by Gary Gordon,Jennifer McNulty Pdf

Matroid theory is a vibrant area of research that provides a unified way to understand graph theory, linear algebra and combinatorics via finite geometry. This book provides the first comprehensive introduction to the field which will appeal to undergraduate students and to any mathematician interested in the geometric approach to matroids. Written in a friendly, fun-to-read style and developed from the authors' own undergraduate courses, the book is ideal for students. Beginning with a basic introduction to matroids, the book quickly familiarizes the reader with the breadth of the subject, and specific examples are used to illustrate the theory and to help students see matroids as more than just generalizations of graphs. Over 300 exercises are included, with many hints and solutions so students can test their understanding of the materials covered. The authors have also included several projects and open-ended research problems for independent study.

Computational Oriented Matroids

Author : Jürgen Bokowski
Publisher : Cambridge University Press
Page : 294 pages
File Size : 51,6 Mb
Release : 2006-05-08
Category : Computers
ISBN : 9780521849302

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Computational Oriented Matroids by Jürgen Bokowski Pdf

Oriented matroids play the role of matrices in discrete geometry, when metrical properties, such as angles or distances, are neither required nor available. Thus they are of great use in such areas as graph theory, combinatorial optimization and convex geometry. The variety of applications corresponds to the variety of ways they can be defined. Each of these definitions corresponds to a differing data structure for an oriented matroid, and handling them requires computational support, best realised through a functional language. Haskell is used here, and, for the benefit of readers, the book includes a primer on it. The combination of concrete applications and computation, the profusion of illustrations, many in colour, and the large number of examples and exercises make this an ideal introductory text on the subject. It will also be valuable for self-study for mathematicians and computer scientists working in discrete and computational geometry.

Topics in Matroid Theory

Author : Leonidas S. Pitsoulis
Publisher : Springer Science & Business Media
Page : 138 pages
File Size : 43,5 Mb
Release : 2013-10-24
Category : Mathematics
ISBN : 9781461489573

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Topics in Matroid Theory by Leonidas S. Pitsoulis Pdf

Topics in Matroid Theory provides a brief introduction to matroid theory with an emphasis on algorithmic consequences.Matroid theory is at the heart of combinatorial optimization and has attracted various pioneers such as Edmonds, Tutte, Cunningham and Lawler among others. Matroid theory encompasses matrices, graphs and other combinatorial entities under a common, solid algebraic framework, thereby providing the analytical tools to solve related difficult algorithmic problems. The monograph contains a rigorous axiomatic definition of matroids along with other necessary concepts such as duality, minors, connectivity and representability as demonstrated in matrices, graphs and transversals. The author also presents a deep decomposition result in matroid theory that provides a structural characterization of graphic matroids, and show how this can be extended to signed-graphic matroids, as well as the immediate algorithmic consequences.

Matroid Theory

Author : James G. Oxley
Publisher : Oxford University Press, USA
Page : 550 pages
File Size : 45,7 Mb
Release : 2006
Category : Mathematics
ISBN : 0199202508

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Matroid Theory by James G. Oxley Pdf

The study of matroids is a branch of discrete mathematics with basic links to graphs, lattices, codes, transversals, and projective geometries. Matroids are of fundamental importance in combinatorial optimization and their applications extend into electrical engineering and statics. This incisive survey of matroid theory falls into two parts: the first part provides a comprehensive introduction to the basics of matroid theory while the second treats more advanced topics. The book contains over five hundred exercises and includes, for the first time in one place, short proofs for most of the subjects' major theorems. The final chapter lists sixty unsolved problems and details progress towards their solutions.

Matroid Theory

Author : László Lovász,András Recski
Publisher : North Holland
Page : 448 pages
File Size : 51,7 Mb
Release : 1985
Category : Science
ISBN : UOM:39015037748509

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Matroid Theory by László Lovász,András Recski Pdf

Auctions, Market Mechanisms and Their Applications

Author : Sanmay Das,Michael Ostrovsky,David Pennock,Boleslaw K. Szymanski
Publisher : Springer Science & Business Media
Page : 116 pages
File Size : 46,9 Mb
Release : 2009-07-31
Category : Computers
ISBN : 9783642038211

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Auctions, Market Mechanisms and Their Applications by Sanmay Das,Michael Ostrovsky,David Pennock,Boleslaw K. Szymanski Pdf

These proceedings present the technical contributions to the First Conference on A- tions, Market Mechanisms, and Their Applications (AMMA), held May 8-9, 2009 in Boston, Massachusetts, USA. The conference was devoted to issues that arise in all stages of deploying a market mechanism to solve a problem, including theoretical and empirical examinations. In addition to more traditional academic papers, the conf- ence placed emphasis on experiences from the real world, including case studies and new applications. The main goal of AMMA was to explore the synergy required for good mechanism design. This includes an understanding of the economic and game-theoretic issues, the ability to design protocols and algorithms for realizing desired outcomes, and the knowledge of specific institutional details that are important in practical applications. We were lucky enough to attract papers and talks from economists and computer scientists, theorists and empiricists, academics and practitioners. The program, as reflected in these proceedings, ranged from fundamental theory on auctions and m- kets to empirical design and analysis of matching mechanisms, peer-to-peer-systems, and prediction markets.

Matroid Theory and Its Applications

Author : Adriano Barlotti
Publisher : Unknown
Page : 434 pages
File Size : 55,5 Mb
Release : 1982
Category : Matroids
ISBN : UOM:39015014353182

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Matroid Theory and Its Applications by Adriano Barlotti Pdf