Abstract: A message passing scheme for MAP inference on Markov Random Fields based on a message computation using an intermediate input vector I, an output message vector M, an auxiliary seed vector S, all of equal length N, and a pairwise function r=d(x,y), where r,x,y are real numbers, includes: for each element j of vector S, do S(j)=j consider an index distance ?=2?floor(log2(N)); repeat while ?>0 for each index of vector I, namely i, do in parallel: consider the set of all indices within distance A from a given i, augmented by i; for every k belonging to this set, calculate its distance from i using the function: d(i,k)+I(S(k)); find the minimum distance and call n the index corresponding to this minimum distance do S(i)=S(n) ?=floor (?/2) for each j of vector M, do M(j)=I(S(j))+d(j,S(j)).