Algorithms for Finding Maximal-Scoring Segment Sets

We examine the problem of finding maximal-scoring sets of disjoint regions in a sequence of scores. The problem arises in DNA and protein segmentation, and in post-processing of sequence alignments. Our key result states a simple recursive relationship between maximal-scoring segment sets. The statement leads to an algorithm that finds such a k-set of segments in a sequence of length n in O(nk) time. We describe linear-time algorithms for finding optimal segment sets using different criteria for choosing k, as well as an algorithm for finding an optimal set of k segments in O(nlog n) time, independently of k. We apply our methods to the identification of non-coding RNA genes in thermophiles.