Programming in Networks and Graphs: On The Combinatorial Background And Near-Equivalence Of Network Flow And Matching Algorithms: 300 (Lecture Notes in Economics and Mathematical Systems) - Softcover

Derigs, Ulrich

 
9783540189695: Programming in Networks and Graphs: On The Combinatorial Background And Near-Equivalence Of Network Flow And Matching Algorithms: 300 (Lecture Notes in Economics and Mathematical Systems)
Softcover
ISBN 10: 3540189696 ISBN 13: 9783540189695
Verlag: Springer, 2013

Inhaltsangabe

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.

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Reseña del editor

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.

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Verlag
Springer
Erscheinungsdatum
2013
Sprache
Englisch
ISBN 10 
3540189696
ISBN 13 
9783540189695
Einband
Tapa blanda
Anzahl der Seiten
328
Kontakt zum Hersteller
Nicht verfügbar
Verantwortliche Person
CMN Printpool Inh. Mathis Neumann
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Friedrich-Karl-Str. 9
Hamburg
Deutschland

Weitere beliebte Ausgaben desselben Titels

9780387189697: Programming in Networks and Graphs: On the Combinatorial Background and Near-Equivalence of Network Flow and Matching Algorithms (Lecture Notes in Economics & Mathematical Systems)

Vorgestellte Ausgabe

ISBN 10:  0387189696 ISBN 13:  9780387189697
Verlag: Springer Verlag, 1988
Softcover