Matroid Theory and its Applications in Electric Network Theory and in Statics - Andras Recski

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

(Autor)

Buch | Softcover
XIII, 533 Seiten
2013 | 1. Softcover reprint of the original 1st ed. 1989
Springer Berlin (Verlag)
978-3-662-22145-7 (ISBN)
106,99 inkl. MwSt
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.

ONE.- 1 Basic concepts from graph theory.- 2 Applications.- 3 Planar graphs and duality.- 4 Applications.- 5 The theorems of König and Menger.- 6 Applications.- TWO.- 7 Basic concepts in matroid theory.- 8 Applications.- 9 Algebraic and geometric representation of matroids.- 10 Applications.- 11 The sum of matroids I.- 12 Applications.- 13 The sum of matroids II.- 14 Applications.- 15 Matroids induced by graphs.- 16 Applications.- 17 Some recent results in matroid theory.- 18 Applications.- Appendix 1 Some important results in chronological order.- Appendix 2 List of the Boxes.- Appendix 3 List of the Algorithms.- Appendix 4 Solutions to the Exercises and Problems.

Erscheint lt. Verlag 3.10.2013
Reihe/Serie Algorithms and Combinatorics
Zusatzinfo XIII, 533 p.
Verlagsort Berlin
Sprache englisch
Maße 170 x 244 mm
Gewicht 933 g
Themenwelt Mathematik / Informatik Mathematik Graphentheorie
Schlagworte algorithm • algorithms • combinatorics • Computer • Discrete Mathematics • Network • statics
ISBN-10 3-662-22145-4 / 3662221454
ISBN-13 978-3-662-22145-7 / 9783662221457
Zustand Neuware
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