Abstract

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, find a consecutive subsequence of length at most U with the maximum sum and (ii) given a sequence of real numbers of length n and a lower bound L, find a consecutive subsequence of length at least L with the maximum average. We present an O(n)-time algorithm for the first problem and an O(n log L)-time algorithm for the second. The algorithms have potential applications in several areas of biomolecular sequence analysis including locating GC-rich regions 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 efficient and able to locate useful (such as GC-rich) regions.

Author Keywords: Algorithm; Efficiency; Maximum consecutive subsequence; Length constraint; Biomolecular sequence analysis; Ungapped local alignment

Article Outline

1. Introduction

2. Applications to biomolecular sequence analysis

2.1. Locating GC-rich regions

2.2. Post-processing sequence alignments

2.3. Annotating multiple sequence alignments

2.4. Computing ungapped local alignments with length constraints

3. Maximum sum consecutive subsequence with length constraints

4. Maximum average consecutive subsequence with length constraints

5. Implementation and preliminary experiments

6. Concluding remarks

Acknowledgements

References