The invention computes the optimum path across a terrain or topology represented by an array of parallel processor cells interconnected between neighboring cells by links extending along different directions to the neighboring cells. Such an array is preferably implemented as a high-speed integrated circuit. The computation of the optimum path is accomplished by, in each cell, receiving stimulus signals from neighboring cells along corresponding directions, determining and storing the identity of a direction along which the first stimulus signal is received, broadcasting a subsequent stimulus signal to the neighboring cells after a predetermined delay time, whereby stimulus signals propagate throughout the array from a starting one of the cells. After propagation of the stimulus signals throughout the array, a master processor traces back from a selected destination cell to the starting cell along an optimum path of the cells in accordance with the identity of the directions stored in each of the cells.