Matroid Applications

Matroid Applications
Author :
Publisher : Cambridge University Press
Total Pages : 377
Release :
ISBN-10 : 9780521381659
ISBN-13 : 0521381657
Rating : 4/5 (59 Downloads)

Synopsis Matroid Applications by : Neil White

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

Matroid Theory and its Applications in Electric Network Theory and in Statics
Author :
Publisher : Springer Science & Business Media
Total Pages : 542
Release :
ISBN-10 : 9783662221433
ISBN-13 : 3662221438
Rating : 4/5 (33 Downloads)

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

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

Theory of Matroids
Author :
Publisher : Cambridge University Press
Total Pages : 341
Release :
ISBN-10 : 9780521309370
ISBN-13 : 0521309379
Rating : 4/5 (70 Downloads)

Synopsis Theory of Matroids by : Neil White

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

Oriented Matroids
Author :
Publisher : Cambridge University Press
Total Pages : 564
Release :
ISBN-10 : 9780521777506
ISBN-13 : 052177750X
Rating : 4/5 (06 Downloads)

Synopsis Oriented Matroids by : Anders Björner

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

Matrices and Matroids for Systems Analysis

Matrices and Matroids for Systems Analysis
Author :
Publisher : Springer Science & Business Media
Total Pages : 500
Release :
ISBN-10 : 3540660240
ISBN-13 : 9783540660248
Rating : 4/5 (40 Downloads)

Synopsis Matrices and Matroids for Systems Analysis by : Kazuo Murota

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

Matroids: A Geometric Introduction

Matroids: A Geometric Introduction
Author :
Publisher : Cambridge University Press
Total Pages : 411
Release :
ISBN-10 : 9780521145688
ISBN-13 : 0521145686
Rating : 4/5 (88 Downloads)

Synopsis Matroids: A Geometric Introduction by : Gary Gordon

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

Computational Oriented Matroids

Computational Oriented Matroids
Author :
Publisher : Cambridge University Press
Total Pages : 294
Release :
ISBN-10 : 9780521849302
ISBN-13 : 0521849306
Rating : 4/5 (02 Downloads)

Synopsis Computational Oriented Matroids by : Jürgen Bokowski

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.

A Source Book in Matroid Theory

A Source Book in Matroid Theory
Author :
Publisher :
Total Pages : 424
Release :
ISBN-10 : UCSD:31822002756054
ISBN-13 :
Rating : 4/5 (54 Downloads)

Synopsis A Source Book in Matroid Theory by : Joseph P. S. Kung

Matroid Theory

Matroid Theory
Author :
Publisher : OUP Oxford
Total Pages : 0
Release :
ISBN-10 : 0199603391
ISBN-13 : 9780199603398
Rating : 4/5 (91 Downloads)

Synopsis Matroid Theory by : James Oxley

This major revision of James Oxley's classic Matroid Theory provides a comprehensive introduction to the subject, covering the basics to more advanced topics. With over 700 exercises and proofs of all relevant major theorems, this book is the ideal reference and class text for academics and graduate students in mathematics and computer science.

Matroid Theory

Matroid Theory
Author :
Publisher : North Holland
Total Pages : 450
Release :
ISBN-10 : UCSD:31822002036515
ISBN-13 :
Rating : 4/5 (15 Downloads)

Synopsis Matroid Theory by : László Lovász