An O(log N) Algorithm to Solve Linear Recurrences on Hypercubes

0 Introduction In their recent IPL paper H.N. Reddy and E.L. Leiss RL94] present an O(log N) algorithm for solving linear recurrences on hypercubic architectures. The authors go to great lengths to construct an algorithm that appears to be correct. First they construct a solution for a completely connected architecture (say a CREW PRAM) and remark that it is similar to a parallel preex computation. This solution is then transformed into one that runs eeciently on a hypercube. However, O(log N) algorithms for parallel preex on the hypercube are known in the literature (eg. MP89] and RS90]). Therefore, constructing an O(log N) algorithm for the linear recurrence problem amounts to no more than showing that the problem is reducible to a parallel preex sum problem, which we proceed to do.