Hari N. Reddy

An O (log N ) algorithm to solve linear recurrences on hypercubes

Abstract The hypercube is one of the most appealing and successful topologies among the interconnection networks designed for parallel processing applications. Linear recurrences arise frequently in many useful and important engineering and scientific applications. Consequently, fast parallel algorithms to solve linear recurrences offer significant value to the scientific community. In this paper we describe an efficient collision-free algorithm to solve general first order linear recurrences of length N on an N-node hypercube network. The time complexity of this algorithm is shown to be O(log N). For linear recurrences of length s × N where s is an integer > 0, the time complexity is shown to be O(s log N).