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Notice of Retraction
After careful and considered review of the content of this paper by a duly constituted expert committee, this paper has been found to be in violation of IEEE's Publication Principles.
We hereby retract the content of this paper. Reasonable effort should be made to remove all past references to this paper.
The presenting author of this paper has the option to appeal this decision by contacting TPII@ieee.org.
We consider one kind of uncapacitated facility location problem which we call k-product uncapacitated facility location problem with no-fixed costs(k-PUFLPN). The problem can be defined as follows: There is a set of demand points where clients are located and a set of potential sites where facilities of unlimited capacities can be set up. There are k different kinds of products. Each client needs to be supplied with k kinds of products by a set of k different facilities and each facility can be set up to supply only a distinct product with no fixed cost. There is a non-negative cost of shipping goods between each pair of locations. These costs are assumed to be symmetric and satisfy the triangle inequality. We want to select a set of facilities to be opened and their designated products and to find an assignment for each client to a set of k facilities so as to minimize the sum of the shipping costs. In this paper, we propose an approximation algorithm with a performance guarantee of (3/2) k -1 for the k-PUFLPN.