634 Approximation Algorithms Fall Semester , 2003 Lecture 19 : Nov 12 , 2003
نویسنده
چکیده
Recall that in the uncapacitated facility location problem we are given a set F of facilities and a set C of clients. There is a specified cost of opening a facility and specified distance between every pair i, j ∈ F ∪C. We assume that the distances satisfy the triangle inequality. The goal is to identify a set of facilities in F to serve all the clients in C such that the total facility and connection cost is minimized. Observe that a given a set of open facilities, serving each client by the nearest open facility minimizes the connection cost. Let S∗: set of open facilities in the global optimum solution S: set of open facilities in the local optimum solution cj : connection cost of client j in S ∗ cj: connection cost of client j in S N∗(i): set of clients assigned to facility i in S∗ N(i): set of clients assigned to facility i in S fi: cost of opening facility i
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