Towards Parallel Sorting with Sampling Techniques on non Homogeneous Clusters

In this note we introduce some parallel in−core technique for sorting integer keys which is based on the regular sampling technique. We sketch an algorithm which is devoted to clusters of non homogeneous processors (the speeds of processors and/or the speeds to access distributed disks in the clusters are correlated by a multiplicative constant factor and/or the bandwidth of the underlying network interconnected processors by a switch is not to be supposed to be identical in whole the network). This note is devoted to show that sampling techniques are independant (in some way) to the architecture of the computing system on which we run the sorting program. In our case, "independence" means that we can guarantee load 5− Sorting on two sorts of processors with the sampling technique In this section we exemplify a sorting problem for which we have n data to sort on a system of p=4 processors: two processors are running at 400Mhz and two processors are running at 200Mhz. Moreover assume that the fastest processors are labelled from 1 to 2 and the slower to 3 to 4. Thus, the speed ratio is k = 400 200 = 2. Let n 1 be the number of data that the processors at 400Mhz should have to deal with to ensure optimal load balancing and let n 2 be the number of data that processors at 200MHz should deal with to ensure optimal load balancing on the 4 processors system. We have: ( 1) n1 + n2 = n, (2) n1 − k.n2 = 0. From the two previous equations, it is not difficult to derive: n 2 = n k+1 and n 1 = k.n k+1 In the remainder of the note we impose that n 1 , n 2 ∈ א . To go further in our case study we choose now n = 72⇒ n 1 = 48, n 2 = 24 . That is to say that the two fastest processors have 24 data each and the slower processors have 12