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

We present an efficient message passing method for 0-1 integer linear programs. Our algorithm is based on a decomposition of the original problem into subproblems that are represented as binary decision diagrams. The resulting Lagrangean dual is solved iteratively by a series of efficient block coordinate ascent steps. Our method combines techniques from dedicated solvers developed for subclasses of combinatorial problems in structured prediction with the generality of 0-1 integer linear programming. In particular, our solver has linear iteration complexity w.r.t. the problem decomposition size and empirically needs a moderate number of iterations to converge. We present experimental results on combinatorial problems from MAP inference for Markov Random Fields, graph matching, discrete tomography and cell tracking for developmental biology and show competitive performance.