Finding All Minimal Maximum Subsequences in Parallel

Abstract

A maximum contiguous subsequence of a real-valued sequence is a contiguous subsequence with the maximum cumulative sum. A minimal maximum contiguous subsequence is a minimal contiguous subsequence among all maximum ones of the sequence. We have previously designed and implemented a domain-decomposed parallel algorithm on cluster systems with Message Passing Interface that finds all successive minimal maximum subsequences of a random sample sequence from a normal distribution with negative mean. The parallel cluster algorithm employs the theory of random walk to derive an approximate probabilistic length upper bound for overlapping subsequences in an appropriate probabilistic setting, which is incorporated in the algorithm to facilitate the concurrent computation of all minimal maximum subsequences in hosting processors. We present in this article: (1) a generalization of the parallel cluster algorithm with improvements for input of arbitrary real-valued sequence, and (2) an empirical study of the speedup and efficiency achieved by the parallel algorithm with synthetic normally-distributed random sequences.