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Solving the uncapacitated facility location problem using message passing algorithms

Solving the uncapacitated facility location problem using message passing algorithms

This video was recorded at 13th International Conference on Artificial Intelligence and Statistics (AISTATS), Sardinia 2010. The Uncapacitated Facility Location Problem (UFLP) is one of the most widely studied discrete location problems, whose applications arise in a variety of settings. We tackle the UFLP using probabilistic inference in a graphical model - an approach that has received little attention in the past. We show that the fixed points of max-product linear programming (MPLP), a convexified version of the max-product algorithm, can be used to construct a solution with a 3-approximation guarantee for metric UFLP instances. In addition, we characterize some scenarios under which the MPLP solution is guaranteed to be globally optimal. We evaluate the performance of both max-sum and MPLP empirically on metric and non-metric problems, demonstrating the advantages of the 3-approximation construction and algorithm applicability to non-metric instances.

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