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) - Tapa blanda

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)
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ISBN 10: 3540189696 ISBN 13: 9783540189695
Editorial: Springer, 2013

Sinopsis

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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Editorial
Springer
Año de publicación
2013
Idioma
Inglés
ISBN 10 
3540189696
ISBN 13 
9783540189695
Encuadernación
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Número de páginas
328
Contacto del fabricante
no disponible
Persona responsable
CMN Printpool Inh. Mathis Neumann
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Alemania

Otras ediciones populares con el mismo título

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)

Edición Destacada

ISBN 10:  0387189696 ISBN 13:  9780387189697
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