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Degeneracy Graphs and the Neighbourhood Problem

  • Book
  • © 1986

Overview

Authors:
  1. H.-J. Kruse

    1. Fachbereich Wirtschaftswissenschaft, Fernuniversität Hagen, Hagen 1, Germany

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Part of the book series: Lecture Notes in Economics and Mathematical Systems (LNE, volume 260)

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Table of contents (5 chapters)

  1. Front Matter

    Pages N2-VIII
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  2. Introduction

    • H.-J. Kruse
    Pages 1-4

  3. The Concept of Degeneracy

    • H.-J. Kruse
    Pages 4-9

  4. Degeneracy Graphs

    • H.-J. Kruse
    Pages 10-33

  5. On the Number of Nodes of Degeneracy Graphs

    • H.-J. Kruse
    Pages 34-60

  6. A Method to Solve the Neighbourhood Problem

    • H.-J. Kruse
    Pages 61-99

  7. Back Matter

    Pages 101-132
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Keywords

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.

Authors and Affiliations

  • Fachbereich Wirtschaftswissenschaft, Fernuniversität Hagen, Hagen 1, Germany

    H.-J. Kruse

Bibliographic Information

  • Book Title: Degeneracy Graphs and the Neighbourhood Problem

  • Authors: H.-J. Kruse

  • Series Title: Lecture Notes in Economics and Mathematical Systems

  • DOI: https://doi.org/10.1007/978-3-642-49270-9

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1986

  • Softcover ISBN: 978-3-540-16049-6Published: 01 January 1986

  • eBook ISBN: 978-3-642-49270-9Published: 06 December 2012

  • Series ISSN: 0075-8442

  • Series E-ISSN: 2196-9957

  • Edition Number: 1

  • Number of Pages: VIII, 132

  • Number of Illustrations: 15 b/w illustrations

  • Topics: Operations Research/Decision Theory

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