Load-balanced parallel merge sort on distributed memory parallel computers

Abstract

Sort can be speeded up on parallel computers by dividing and computing data individually in parallel. Merge sort can be parallelized, however, the conventional algorithm implemented on distributed memory computers has poor performance due to the successive reduction of the number of active (non-idling) processors by a half, up to one in the last merging stage. This paper presents load-balanced parallel merge sort algorithm where all processors participate in merging throughout the computation. Data are evenly distributed to all processors, and every processor is forced to work in merging phase. Significant enhancement of the performance has been achieved. Our analysis shows the upper bound of the speedup of the merge time as (P -1)= logP. We have had a speedup of 9.6 (upper bound is 10.5) on 32-processor Cray T3E in sorting of 4M 32-bit integers. The same idea can be applied to parallellize other sorting algorithms.