A fast algorithm for computing the n-ary composition of a binary associative operator A fast algorithm is presented that, given a sequence of data items, computes an n-ary operation on all contiguous subsequences of length n, where the n-ary operator is computed as the n-ary composition of a binary associative operator. The algorithm is order M where M is the number of n-ary operations to be performed. The algorithm is of use in the computer vision task of region dilation where a run-length encoding of the region can be grown vertically by or-ring together n-tuples of rows of the region.