A problem in pattern recognition is to find the maximum sum over all rectangular subregions of a given (n n) matrix of real numbers. The problem has one-dimensional (1D) and two-dimensional (2D) versions. For the 1D version, it is to find the maximum sum over all contiguous subvector of a given vector of n real numbers. We give an algorithm for the 1D version running in O(log n) time using O((n)/(log n)) processors on the EREW PRAM, and an algorithm for the 2D version which takes O(log n) time using O((n 3 )/(log n)) processors on the EREW PRAM