Programming in Networks and Graphs (eBook, PDF)
Ulrich Derigs
eBook, PDF

Programming in Networks and Graphs (eBook, PDF)

On the Combinatorial Background and Near-Equivalence of Network Flow and Matching Algorithms

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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 soluti...

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