Edmonds-Karp

General Information

Algorithmic problem: Max-Flow Problems

Type of algorithm: loop
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Abstract View

Invariant: After [math]\displaystyle{ i \ge 0 }[/math] iterations:

1. The flow [math]\displaystyle{ f }[/math] is a fleasible flow.
2. If all upper bounds are integral, [math]\displaystyle{ f }[/math] is integral as well.

Notation: For an [math]\displaystyle{ (s,t) }[/math]-flow, let [math]\displaystyle{ A_f }[/math] denote the set of all arcs that belong to at least one flow-augmenting [math]\displaystyle{ (s,t) }[/math]-path with smallest number of arcs.

Variant:

1. The smallest number of arcs on a flow-aumenting [math]\displaystyle{ (s,t) }[/math]-path increases (non-strictly) monotonously.
2. Whenever that number does not decrease in an iteration, the size of [math]\displaystyle{ A_f }[/math] decreases.

Break condition: There is no flow-augumenting path.