Degeneracy Graphs and the Neighbourhood Problem

H. -J. Kruse

ISBN 10: 3540160493 / ISBN 13: 9783540160496

Published by Springer, Springer, 1986

About this Item

Druck auf Anfrage Neuware - Printed after ordering - 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.

Seller Inventory # 9783540160496

Bibliographic Details

• Title: Degeneracy Graphs and the Neighbourhood Problem
• Publisher: Springer, Springer
• Publication Date: 1986
• Language: English
• ISBN 10: 3540160493
• ISBN 13: 9783540160496
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 235W x 155H x 9D millimeters 235 millimeters width by 155 millimeters height by 9 millimeters depth
• Weight: 230 grams

About this title

Synopsis

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.