Min - Cost Flow Algorithms 10 . 1 Shortest Augmenting Paths : Unit Capacity Networks
نویسنده
چکیده
Proof: (by induction). We want to show that one SAP doesn’t introduce negative cycles in Gf . Initially there are no negative cost cycles. Feasible prices can be computed by using shortest path distances from s. After finding the shortest s-t path, it has reduced cost 0. Every arc on the path has reduced length 0. This demonstrates that the triangle inequality property is tight on shortest path edges. When we augment along the path, therefore, the residual backwards arcs we create are of reduced cost 0. Therefore in the new Gf , the price function is still feasible. Furthermore, there are:
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