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Lecture Notes in Economics and Mathematical Systems

Degeneracy Graphs and the Neighbourhood Problem

Authors: Kruse, H.-J.

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About this book

A few years ago nobody would have anticipated that in connection with degeneracy in Linear Programming quite a new field. could originate. In 1976 a very simple question has been posed: in the case an extreme­ pOint (EP) of a polytope is degenerate and the task is to find all neighbouring EP's of the degenerate EP, is it necessary to determine all basic solutions of the corresponding equalities system associated with the degenerate EP -in order to be certain to determine all neighbours of this EP? This question implied another one: Does there exists a subset of the mentioned set of basic solutions such that it suffices to find such a subset in order to determine all neighbours? The first step to solve these questions (which are motivated in the first Chapter of this book) was to define a graph (called degeneracy graph) the nodes of which correspond to the basic solutions. It turned out that such a graph has some special properties and in order to solve the above questions firstly these properties had to be investigated. Also the structure of degeneracy graphs playes hereby an important role. Because the theory of degeneracy graphs was quite new, it was necessary to elaborate first a completely new terminology and to define new notions. Dr.

Table of contents (5 chapters)

Table of contents (5 chapters)

Buy this book

eBook $79.99
price for USA in USD
  • ISBN 978-3-642-49270-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $99.99
price for USA in USD
  • ISBN 978-3-540-16049-6
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Degeneracy Graphs and the Neighbourhood Problem
Authors
Series Title
Lecture Notes in Economics and Mathematical Systems
Series Volume
260
Copyright
1986
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-49270-9
DOI
10.1007/978-3-642-49270-9
Softcover ISBN
978-3-540-16049-6
Series ISSN
0075-8442
Edition Number
1
Number of Pages
VIII, 132
Number of Illustrations
15 b/w illustrations
Topics

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