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(ω), the min-max message update can be obtained using an efficient O(K(ω + 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.

Authors
BibTeX

@InProceedings{SrinivasaMMP,
Title = {Min-Max Propagation},
Author = {Christopher Srinivasa and Inmar Givoni and Siamak Ravanbahksh and Brendan J. Frey},
Year = {2017},
Abstract = {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(ω), the min-max message update can be obtained using an efficient O(K(ω + 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 theworst case load is minimized.},
Journal = {NIPS},
Url = {https://papers.nips.cc/paper/7140-min-max-propagation}
}