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We present a message passing method for 0-1 integer linear programs. Ouralgorithm is based on a decomposition of the original problem into subproblemsthat are represented as binary decision diagrams. The resulting Lagrangean dualis solved iteratively by a series of efficient block coordinate ascent steps.Our method has linear iteration complexity in the size of the decomposition andcan be effectively parallelized. The characteristics of our approach aredesirable towards solving ever larger problems arising in structuredprediction. We present experimental results on combinatorial problems from MAPinference for Markov Random Fields, quadratic assignment, discrete tomographyand cell tracking for developmental biology and show promising performance.

Efficient Message Passing for 0-1 ILPs with Binary Decision Diagrams