Finding maximum on an array processor with a global bus

Abstract

The problem of finding the maximum of a set of values stored one/processor on an n x n array of processors is analyzed. The array has a time-shared global bus in addition to conventional processor-processor links. A two-phase algorithm for finding the maximum is presented that uses conventional links during the first phase and the global bus during the second. This algorithm is faster than algorithms that use either only the global bus or only the conventional links. Two types of interconnection patterns (the eighth nearest neighbor and the fourth nearest neighbor) are analyzed. In both cases it is shown that the time required to find the maximum using the two-phase algorithm is 0(n to the 2/3-power) assuming the propagation speed of the global bus to be a constant independent of the size of the array. In the case where the propagation speed is logarithmic in the number of processors, the time to find the maximum is 0(/n-squared log n/1/3), for both types of arrays. Extensions to q-dimensional arrays show that the two-phase algorithm is superior for any fixed value of q.