11 - Lower Bounds

Abstract

This chapter presents a review of lower bounds. An algorithm achieves the best possible running time for sorting on a particular architecture, to within a constant multiplicative factor. To prove such a property, a lower bound is usually appealed to on the worst-case running time of any parallel sorting algorithm for that architecture. The significance of a lower bound on a problem is that it tells that, in the worst case, no algorithm, regardless of how clever it is, can do fewer operations in solving that problem. By deriving such a bound for a given model of computation, it is, therefore, possible to determine how fast the problem on that model can be solved. The two subsequences are sorted in parallel using the same algorithm, and the resulting subsequences are merged. The running time of the algorithm is determined by the time required to sort the larger of the two subsequences plus the merging time.