Programming in Networks and Graphs | On the Combinatorial Background and Near-Equivalence of Network Flow and Matching Algorithms

Ulrich Derigs

ISBN 10: 3540189696 / ISBN 13: 9783540189695

Published by Springer, 1988

About this Item

Programming in Networks and Graphs | On the Combinatorial Background and Near-Equivalence of Network Flow and Matching Algorithms | Ulrich Derigs | Taschenbuch | Lecture Notes in Economics and Mathematical Systems | xi | Englisch | 1988 | Springer | EAN 9783540189695 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu.

Seller Inventory # 105646265

Bibliographic Details

• Title: Programming in Networks and Graphs | On the Combinatorial Background and Near-Equivalence of Network Flow and Matching Algorithms
• Publisher: Springer
• Publication Date: 1988
• Language: English
• ISBN 10: 3540189696
• ISBN 13: 9783540189695
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 229W x 152H x 18D millimeters 229 millimeters width by 152 millimeters height by 18 millimeters depth
• Weight: 477 grams
• Seller catalogs:
  • Bücher

About this title

Synopsis

Network flow and matching are often treated separately in the literature and for each class a variety of different algorithms has been developed. These algorithms are usually classified as primal, dual, primal-dual etc. The question the author addresses in this work is that of the existence of a common combinatorial principle which might be inherent in all those apparently different approaches. It is shown that all common network flow and matching algorithms implicitly follow the so-called shortest augmenting path. This can be interpreted as a greedy-like decision rule where the optimal solution is built up through a sequence of local optimal solutions. The efficiency of this approach is realized by combining this myopic decision rule with an anticipant organization. The approach of this work is organized as follows. For several standard flow and matching problems the common solution procedures are first reviewed. It is then shown that they all reduce to a common basic principle, that is, they all perform the same computational steps if certain conditions are set properly and ties are broken according to a common rule. Recognizing this near-equivalence of all commonly used algorithms the question of the best method has to be modified - all methods are (only) different implementations of the same algorithm obtained by different views of the problem.