Abstract

We consider the problem of partitioning a sequence of n real numbers into p intervals such that the cost of the most expensive interval, measured with a cost function f is minimized. This problem is of importance for the scheduling of jobs both in parallel and pipelined environments. We develop an efficient dynamic programming algorithm that solves this problem in time O(p(n - p)), which is an improvement of a factor of log p compared to the previous best algorithm. A number of variants of the problem are also considered. We demonstrate how a solution to the partitioning problem can be used to speed up sparse matrix, dense vector multiplication on a SIMD computer.

Citations