Efficient algorithms for locating the length-constrained heaviest segments with applications to biomolecular sequence analysis

We study two fundamental problems concerning the search for interesting regions in sequences:(i)given a sequence of real numbers of length n and an upper bound U摯瑬敳獩 find a consecutive subsequence of lengthat most U withth maximum sum and (ii)given a sequence of real numbers of length n and a lower bound L摯瑬敳獩 find a consecutive subsequence of lengthat least L withth maximum average.We present an O摯瑬敳獩 n捡牯渀 ⴀ琀椀洀攀 愀氀最漀爀椀琀栀洀 昀漀爀 琀栀攀⃻Ā爀猀琀 瀀爀漀戀氀攀洀ഀ਀愀渀搀 愀渀 佤潴汥獳椀 渀 氀漀最 䱣慲潮 -time algorithm for the second.The algorithms have potential applications in several areas of biomolecular sequence analysis including locating GC-richregions in a genomic DNA sequence,post-processing sequence alignments,annotating multiple sequence alignments,and computing length-constrained ungapped local alignment.Our preliminary tests on both simulated and real data demonstrate that the algorithms are very ef ficient and able to locate useful (suchas GC-rich)regions