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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