Fast and space-efficient location of heavy or dense segments in run-length encoded sequences

Authors:
Ronald I. Greenberg
Affiliations:
Loyola University, Chicago, IL
Venue:
COCOON'03 Proceedings of the 9th annual international conference on Computing and combinatorics
Year:
2003

Citing 3
Cited 2

Introduction to Algorithms

Introduction to Algorithms
Efficient Algorithms for Locating the Length-Constrained Heaviest Segments, with Applications to Biomolecular Sequence Analysis

MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
Fast Algorithms for Finding Maximum-Density Segments of a Sequence with Applications to Bioinformatics

WABI '02 Proceedings of the Second International Workshop on Algorithms in Bioinformatics

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

Journal of Computer and System Sciences
Testing Stream Ciphers by Finding the Longest Substring of a Given Density

ACISP '09 Proceedings of the 14th Australasian Conference on Information Security and Privacy

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Abstract

This paper considers several variations of an optimization problem with potential applications in such areas as biomolecular sequence analysis and image processing. Given a sequence of items, each with a weight and a length, the goal is to find a subsequence of consecutive items of optimal value, where value is either total weight or total weight divided by total length. There may also be a specified lower and/or upper bound on the acceptable length of subsequences. This paper shows that all the variations of the problem are solvable in linear time and space even with non-uniform item lengths and divisible items, implying that run-length encoded sequences can be handled in time and space linear in the number of runs. Furthermore, some problem variations can be solved in constant space. Also, these time and space bounds suffice for certain problem variations in which we call for reporting of many "good" subsequences.