Min-Max Propagation.

We study the application of min-max propagation, a variation of belief propagation, for approximate min-max inference in factor graphs. We show that for "any" high-order function that can be minimized in O (omega), the min-max message update can be obtained using an efficient O (K (omega + log (K)) procedure, where K is the number of variables. We demonstrate how this generic procedure, in combination with efficient updates for a family of high-order constraints, enables the application of min-max propagation to efficiently approximate the NP-hard problem of makespan minimization, which seeks to distribute a set of tasks on machines, such that the worst case load is minimized.