12 : Network Flow V - Min - cost flow
نویسنده
چکیده
Let G = (V, E) be a digraph (i.e., a directed graph) with n vertices and m edges, and w : E → IR be a weight function on the edges. A directed cycle is closed walkC = (v0, v1, . . . , vt), where vt = v0 and (vi → vi+1) ∈ E, for i = 0, . . . , t − 1. The average cost of a directed cycle is AvgCost(C) = ω(C)/t = (∑e∈C ω(e)) /t. For each k = 0, 1, . . ., and v ∈ V , let dk(v) denote the minimum length of a walk with exactly k edges, ending at v. So, for each v, we have
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