Many applications involve repeatedly computing the optimal, maximum a posteriori (MAP) configuration of a graphical model as the model changes, often slowly or incrementally over time, e.g., due to input from a user. Small changes to the model often require updating only a small fraction of the MAP configuration, suggesting the possibility of performing updates faster than recomputing from scratch. In this paper we present an algorithm for efficiently performing such updates under arbitrary

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... ges to the model. Our algorithm is within a logarithmic factor of the optimal and is asymptotically never slower than re-computing from-scratch: if a modification to the model requires m updates to the MAP configuration of n random variables, then our algorithm requires O(m log (n/m)) time; re-computing from scratch requires O(n) time. We evaluate the practical effectiveness of our algorithm by considering two problems in genomic signal processing, CpG region segmentation and protein sidechain packing, where a MAP configuration must be repeatedly updated. Our results show significant speedups over recomputing from scratch.