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Information Processing Letters
On the range maximum-sum segment query problem
Discrete Applied Mathematics
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
Finding a maximum-density path in a tree under the weight and length constraints
Information Processing Letters
An improved algorithm for finding a length-constrained maximum-density subtree in a tree
Information Processing Letters
An optimal algorithm for the maximum-density path in a tree
Information Processing Letters
Finding long and similar parts of trajectories
Proceedings of the 17th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
Optimal Randomized Algorithm for the Density Selection Problem
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Information Processing Letters
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
The weight-constrained maximum-density subtree problem and related problems in trees
The Journal of Supercomputing
Finding long and similar parts of trajectories
Computational Geometry: Theory and Applications
The density maximization problem in graphs
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Finding a weight-constrained maximum-density subtree in a tree
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Disjoint segments with maximum density
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part II
On locating disjoint segments with maximum sum of densities
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
FLOPS'12 Proceedings of the 11th international conference on Functional and Logic Programming
The density maximization problem in graphs
Journal of Combinatorial Optimization
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We address a fundamental problem arising from analysis of biomolecular sequences. The input consists of two numbers wmin and wmax and a sequence S of n number pairs (ai,wi) with wi 0. Let segment S(i,j) of S be the consecutive subsequence of S between indices i and j. The density of S(i,j) is d(i,j) = (ai + ai + 1 + \cdots + aj)/(wi + wi + 1 + \cdots + wj)$. The maximum-density segment problem is to find a maximum-density segment over all segments S(i,j) with wmin \leq wi + wi + 1 + \cdots + wj \leq wmax. The best previously known algorithm for the problem, due to Goldwasser, Kao, and Lu [Proceedings of the Second International Workshop on Algorithms in Bioinformatics, R. Guigó and D. Gusfield, eds., Lecture Notes in Comput. Sci. 2452, Springer-Verlag, New York, 2002, pp. 157--171], runs in O(n log(wmax- wmin+1)) time. In the present paper, we solve the problem in O(n) time. Our approach bypasses the complicated right-skew decomposition, introduced by Lin, Jiang, and Chao [J. Comput. System Sci., 65 (2002), pp. 570--586]. As a result, our algorithm has the capability to process the input sequence in an online manner, which is an important feature for dealing with genome-scale sequences. Moreover, for a type of input sequences S representable in O(m) space, we show how to exploit the sparsity of S and solve the maximum-density segment problem for S in O(m) time.