A fast sorting algorithm and its generalization on broadcast communications

Abstract

In this paper, we shall propose a fast algorithm to solve the sorting problem under the broadcast communication model(BCM). The key point of our sorting algorithm is to use successful broadcasts to build broadcasting layers logically and then to distribute the data elements into those logic layers properly. Thus, the number of broadcast conflicts is reduced. Suppose that there are n input data elements and n processors under BCM are available. We show that the average time complexity of our sorting algorithm is Θ(n). In addition, we expand this result to the generalized sorting, that is, nding the rst k largest elements with a sorted sequence among n elements. The analysis of the generalization builds a connection between the two special cases which are maximum nding and sorting. We prove that the average time complexity for nding the rst k largest numbers is Θ(k + log (n - k)).