Efficient parallel algorithms for maximum-density segment problem

One of the fundamental problems involving DNA sequences is to find high density segments of certain widths, for example, those regions with intensive guanine and cytosine (GC). Formally, given a sequence, each element of which has a value and a width, the maximum-density segment problem asks for the segment with the maximum density while satisfying minimum and possibly maximum width constraints. While several linear-time sequential algorithms have emerged recently due to its primitive-like utility, to our knowledge, no nontrivial parallel algorithm has yet been proposed for this topical problem. In this paper, we propose an O(log² n)-time CREW PRAM algorithm using n processors to solve the generalized maximum-density problem, with a minimum width constraint and non-uniform widths. Besides, we describe an efficient implementation of the parallel algorithm on manycore GPUs (nVIDIA GeForce GTX 280), taking advantage of the full programmability of CUDA. This algorithm can process up to million-size sequence within a second using an nVIDIA GeForce GTX 280, thus demonstrating the practicality of this algorithm as a basic primitive for scientists. This may also indicate suitability of modern GPU architectures as implementation platform for certain PRAM algorithms.