Network Design Foundations Fall 2011 Lecture 10 Instructor : Mohammad
نویسنده
چکیده
Suppose we are given a graph G = (V, E), with a metric cost function c over the edges. (that is, a cost function which satisfies the triangle inequality). Suppose we have a set of clients D ⊆ V. Consider that facilities can be opened at any client vertex. Each client i ∈ D has an associated demand di. There are no facility opening costs. The task is to connect each client to a facility. Let us call this the connection cost. Additionally, all the opened facilities need to be connected to each other, via higher-cost edges. Let us call this second cost the Steiner cost. Let a set of facilities F ⊆ D be the set of opened facilities. Formally, we need to minimize the following objective function:
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