Algorithms for computing the length-constrained max-score segments with applications to DNA copy number data analysis

Authors:
Hsiao-Fei Liu;Peng-An Chen;Kun-Mao Chao
Affiliations:
Department of Computer Science and Information Engineering, National Taiwan University, Taipei, Taiwan;Department of Computer Science and Information Engineering, National Taiwan University, Taipei, Taiwan;Dept. of Computer Sci. and Information Eng., National Taiwan Univ., Taipei, Taiwan and Graduate Institute of Biomedical Electronics and Bioinformatics and Graduate Institute of Networking and Mult ...
Venue:
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Year:
2007

Citing 14
Cited 0

Differential morphology

Nonlinear image processing
The Design and Analysis of Computer Algorithms

The Design and Analysis of Computer Algorithms
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
An Optimal Algorithm for the Maximum-Density Segment Problem

SIAM Journal on Computing
Linear-time algorithms for computing maximum-density sequence segments with bioinformatics applications

Journal of Computer and System Sciences
Fast algorithms for finding disjoint subsequences with extremal densities

Pattern Recognition
A geometric framework for solving subsequence problems in computational biology efficiently

SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
More algorithms for all-pairs shortest paths in weighted graphs

Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Necklaces, convolutions, and X + Y

ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
An O(n3 (loglogn/logn)5/4) time algorithm for all pairs shortest paths

ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
An optimal algorithm for maximum-sum segment and its application in bioinformatics

CIAA'03 Proceedings of the 8th international conference on Implementation and application of automata
Efficient calculation of interval scores for DNA copy number data analysis

RECOMB'05 Proceedings of the 9th Annual international conference on Research in Computational Molecular Biology
An algorithm for a generalized maximum subsequence problem

LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics

Quantified Score

Hi-index	0.00

Visualization

Abstract

Given a sequence of n real numbers A = (a1, a2,..., an), two integers L and U with 1 ≤ L ≤ U ≤ n, and a score function f : IR+ × IR → IR, the LENGTH-CONSTRAINED MAX-SCORE SEGMENT PROBLEM is to find a segment A[i, j] = (ai, ai+1,..., aj) maximizing f(j - i + 1, Σh=ij ah) subject to j - i + 1 ∈ [L, U]. In this paper, we solve the LENGTH-CONSTRAINED MAX-SCORE SEGMENT PROBLEM for the case where the given score function f(l, w) = w/r√l for any constant r 1. Our algorithm runs in O(n T(L1/2)/L1/2) time, where T(n′) is the time required to solve the all-pairs shortest paths problem on a graph of n′ nodes. By the latest result of Chan [7], T(n′) = O(n′3 (log log n′)3/(log n′)2), so our algorithm runs in subquadratic time O(nL (log log L)3/(log L)2). Lipson et al. [21] studied a more restricted case where the score function f(l,w) = w/2√l and there are no length constraints, i.e., L = 1 and U = n. They also showed how to apply their algorithm to analyzing DNA copy number data. However, their algorithm takes Ω(n2) time in the worst situation. Since the length lower bound L for the case considered by Lipson et al. is a constant, our algorithm solves it in O(n) time.