Fast Algorithms for Finding Maximum-Density Segments of a Sequence with Applications to Bioinformatics

摘要

We study an abstract optimization problem arising from biomolecular sequence analysis. For a sequence A = of real numbers, a segment 5 is a consecutive subsequence . The width of S is j ― i + 1, while the density is (Σ_(i≤k≤j)a_k)/(j ― i+1). The maximum-density segment problem takes A and two integers L and U as input and asks for a segment of A with the largest possible density among those of width at least L and at most U. If U = n (or equiva-lently, U = 2L ― 1), we can solve the problem in O(n) time, improving upon the O(n log L)-time algorithm by Lin, Jiang and Chao for a general sequence A. Furthermore, if U and L are arbitrary, we solve the problem in O(n + n log(U ― L + 1)) time. There has been no nontrivial result for this case previously. Both results also hold for a weighted variant of the maximum-density segment problem.