Fast parallel algorithms for forecasting

This paper presents two parallel algorithms for forecasting implemented on a linear array and a tree model [1]. Both the algorithms are based on the weighted moving average technique [2,3]. Given that m and n are the numbers of the input observed data values and the numbers of weights, respectively, the algorithm on a linear array of n processors requires m + 1 steps and that on a tree model with (2n − 1) processors (n being a power of 2), needs (m − n + 2) + log2n steps. It has also been shown how the corresponding algorithms can be extended to the case when the number of available processors is less than n (for a linear array) or 2n − 1 (for a tree model). The corresponding algorithms mapped on an ST-array (Store and Trigger array with p processors, p ≤ n) [4] and an ST-tree (Store and Trigger tree with 2p − 1 processors, p ≤ n, p being a power of 2) require n/p(m − n + 1) + p − 1 and n/p[(m − n + 2) + log2p] steps, respectively.