The Uncapacitated Facility Location Prob- lem (UFLP) is one of the most widely stud- ied discrete location problems, whose appli- cations arise in a variety of settings. We tackle the UFLP using probabilistic infer- ence in a graphical model- an approach that has received little attention in the past. We show that the fi xed points of max-product linear programming (MPLP), a convexifi ed 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 eval- uate the performance of both max-sum and MPLP empirically on metric and non-metric problems, demonstrating the advantages of the 3-approximation construction and algo- rithm applicability to non-metric instances.

Message Passing Algorithms..pdf

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