Abstract
In a regular matroidM=(E,C) we discuss two different approaches to group matroid flows. By showing that these two approaches are equivalent we set up a decomposition theory for group matroid flows and derive two algorithms for decomposing group matroid flows. The second one finds so-called positive decomposition, a fact which is highly important in applications.
By specializing the results to graphic and co-graphic matroids we generalize some well known results of real-valued network flow theory to group network flows and derive some new results for tensions.
Zusammenfassung
Wir betrachten zwei verschiedene Ansätze für Gruppenflüsse in einem regulären MatroidM=(E,C). Indem wir zeigen, daß diese beiden Ansätze äquivalent sind, erhalten wir eine Zerlegungstheorie für Matroidflüsse in regulären Matroiden und leiten daraus zwei Algorithmen zur Zerlegung von Matroidflüssen ab. Der zweite Algorithmus findet eine sogenannte positive Zerlegung, eine Tatsache, die für Anwendungen sehr wichtig ist. Durch Spezialisierung der Resultate auf graphische und cographische Matroide verallgemeinern wir einige bekannte Resultate der reellwertigen Netzwerkflußtheorie auf Gruppen-Netzwerkflüsse und erhalten neue Resultate für Spannungsprobleme.
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This research was supported in part by the Department of Mathematics at the University of Köln, Federal Republic of Germany.
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Hamacher, H. Decomposition of group flows in regular matroids. Computing 29, 113–133 (1982). https://doi.org/10.1007/BF02249936
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DOI: https://doi.org/10.1007/BF02249936