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

Authors:
Michael Goldwasser;Ming-Yang Kao;Hsueh-I Lu
Affiliations:
-;-;-
Venue:
WABI '02 Proceedings of the Second International Workshop on Algorithms in Bioinformatics
Year:
2002

Citing 2
Cited 7

Programming pearls

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

Journal of Computer and System Sciences - Computational biology 2002

Linear-time algorithm for finding a maximum-density segment of a sequence

Information Processing Letters
Linear-time algorithms for computing maximum-density sequence segments with bioinformatics applications

Journal of Computer and System Sciences
Maximum segment sum is back: deriving algorithms for two segment problems with bounded lengths

PEPM '08 Proceedings of the 2008 ACM SIGPLAN symposium on Partial evaluation and semantics-based program manipulation
Fast and space-efficient location of heavy or dense segments in run-length encoded sequences

COCOON'03 Proceedings of the 9th annual international conference on Computing and combinatorics
The weight-constrained maximum-density subtree problem and related problems in trees

The Journal of Supercomputing
Finding a weight-constrained maximum-density subtree in a tree

ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Note: Finding a length-constrained maximum-sum or maximum-density subtree and its application to logistics

Discrete Optimization

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Abstract

We study an abstract optimization problem arising from biomolecular sequence analysis. For a sequence A = 驴a1, a2, . . . , an驴 of real numbers, a segment S is a consecutive subsequence 驴ai, ai+1, . . . , aj驴. The width of S is j - i + 1, while the density is (驴i驴k驴jak)/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 equivalently, 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.