Abstract
In this paper, we propose to study the famous maximum sum segment problem on a sequence consisting of n uncertain numbers, where each number is given as an interval characterizing its possible value. Given two integers L and U, a segment of length between L and U is called a potential maximum sum segment if there exists a possible assignment of the uncertain numbers such that, under the assignment, the segment has maximum sum over all segments of length between L and U. We define the maximum sum segment with uncertainty problem, which consists of two sub-problems: (1) reporting all potential maximum sum segments; (2) counting the total number of those segments. For L = 1 and U = n, we propose an O(n + K)-time algorithm and an O(n)-time algorithm, respectively, where K is the number of potential maximum sum segments. For general L and U, we give an O(n(U − L))-time algorithm for either problem.
Research supported by the National Science Council under the Grants No. NSC-98-2221-E-001-008 and NSC-98-2221-E-001-008.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Altschul, S., Gish, W., Miller, W., Myers, E., Lipman, D.: Basic local alignment search tool. Journal of Molecular Biology 215, 403–410 (1990)
Barhardi, G.: Isochores and the evolutionary genomics of vertebrates. Gene 241, 3–17 (2000)
Bentley, J.: Programming pearls: algorithm design techniques. Communications of the ACM 27(9), 865–873 (1984)
Bernardi, G., Bernardi, G.: Compositional constraints and genome evolution. Journal of Molecular Evolution 24, 1–11 (1986)
Davuluri, R., Grosse, I., Zhang, M.: Computational identification of promoters and first exons in the human genome. Nature Genetics 29, 412–417 (2001)
Fan, T.-H., Lee, S., Lu, H.-I., Tsou, T.-S., Wang, T.-C., Yao, A.: An Optimal Algorithm for Maximum-Sum Segment and Its Application in Bioinformatics Extended Abstract. In: Ibarra, O.H., Dang, Z. (eds.) CIAA 2003. LNCS, vol. 2759, pp. 251–257. Springer, Heidelberg (2003)
Fariselli, P., Finelli, M., Marchignoli, M., Martelli, P.L., Rossi, I., Casadio, R.: Maxsubseq: An algorithm for segment-length optimization. The case study of the transmembrane spanning segments. Bioinformatics 19, 500–505 (2003)
Gabow, H.N., Bentley, J.L., Tarjan, R.E.: Scaling and related techniques for geometry problems. In: 16th Annual ACM Symposium on Theory of Computing, pp. 135–143. ACM Press, New York (1984)
Hannenhalli, S., Levy, S.: Promoter prediction in the human genome. Bioinformatics 17, S90–S96 (2001)
Huang, X.: An algorithm for identifying regions of a DNA sequence that satisfy a content requirement. Computer Applications in Biosciences 10(3), 219–225 (1994)
Lin, Y.-L., Jiang, T., Chao, K.-M.: Efficient algorithms for locating the length-constrained heaviest segments, with applications to biomolecular sequence analysis. Journal of Computer and System Sciences 65(3), 570–586 (2002)
Miklós, C.: Maximum-scoring segment sets. IEEE/ACM Transations on Computatonal Biology and Bioinformatics 1(4), 139–150 (2004)
Walder, R., Garrett, M., McClain, A., Beck, G., Brennan, T., Kramer, N., Kanis, A., Mark, A., Rapp, A., Sheffield, V.: Short tandem repeat polymorphic markers for the rat genome from marker-selected libraries associated with complex mammalian phenotypes. Mammallian Genome 9, 1013–1021 (1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Yu, HI., Lin, TC., Lee, D.T. (2011). Finding Maximum Sum Segments in Sequences with Uncertainty. In: Asano, T., Nakano, Si., Okamoto, Y., Watanabe, O. (eds) Algorithms and Computation. ISAAC 2011. Lecture Notes in Computer Science, vol 7074. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25591-5_75
Download citation
DOI: https://doi.org/10.1007/978-3-642-25591-5_75
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-25590-8
Online ISBN: 978-3-642-25591-5
eBook Packages: Computer ScienceComputer Science (R0)