Parallel sorting by regular sampling

ABSTRACT A new parallel sorting algorithm suitable for MIMD multiprocessors is presented. The algorithm reduces memory and bus contention, which many parallel sorting algorithms suffer from, by using a regular sampling of the data to ensure good pivot selection. For n data elements to be sorted and p processors, when n ≥ p 3 the algorithm is shown to be asymptotically optimal. In theory, the algorithm is within a factor of two of achieving ideal load balancing. In practice, there is almost perfect partitioning of work. On a variety of shared and distributed memory machines, the algorithm achieves better than half-linear speedups. -4

A Domain Decomposition Strategy for Alignment of Multiple Biological Sequences on Multiprocessor Platforms

Multiple Sequences Alignment (MSA) of biological sequences is a fundamental problem in computational biology due to its critical significance in wide ranging applications including haplotype reconstruction, sequence homology, phylogenetic analysis, and prediction of evolutionary origins. The MSA problem is considered NP-hard and known heuristics for the problem do not scale well with increasing number of sequences. On the other hand, with the advent of new breed of fast sequencing techniques it is now possible to generate thousands of sequences very quickly. For rapid sequence analysis, it is therefore desirable to develop fast MSA algorithms that scale well with the increase in the dataset size. In this paper, we present a novel domain decomposition based technique to solve the MSA problem on multiprocessing platforms. The domain decomposition based technique, in addition to yielding better quality, gives enormous advantage in terms of execution time and memory requirements. The proposed strategy allows to decrease the time complexity of any known heuristic of O(N)^x complexity by a factor of O(1/p)^x, where N is the number of sequences, x depends on the underlying heuristic approach, and p is the number of processing nodes. In particular, we propose a highly scalable algorithm, Sample-Align-D, for aligning biological sequences using Muscle system as the underlying heuristic. The proposed algorithm has been implemented on a cluster of workstations using MPI library. Experimental results for different problem sizes are analyzed in terms of quality of alignment, execution time and speed-up.Comment: 36 pages, 17 figures, Accepted manuscript in Journal of Parallel and Distributed Computing(JPDC

On the Versatility of Parallel Sorting by Regular Sampling

Parallel sorting algorithms have already been proposed for a variety of multiple instruction streams, multiple data streams (MIMD) architectures. These algorithms often exploit the strengths of the particular machine to achieve high performance. In many cases, however, the existing algorithms cannot achieve comparable performance on other architectures. Parallel Sorting by Regular Sampling (PSRS) is an algorithm that is suitable for a diverse range of MIMD architectures. It has good load balancing properties, modest communication needs and good memory locality of reference. If there are no duplicate keys, PSRS guarantees to balance the work among the processors within a factor of two of optimal in theory, regardless of the data value distribution, and within a few percent of optimal in practice. This paper presents new theoretical and empirical results for PSRS. The theoretical analysis of PSRS is extended to include a lower bound and a tighter upper bound on the work done by a process..