Abstract
We are given a sequence A of n real numbers which is to be preprocessed. In the Range Maximum-Sum Segment Query (RMSQ) problem, a query is comprised of two intervals [i,j] and [k,l] and our goal is to return the maximum-sum segment of A whose starting index lies in [i,j] and ending index lies in [k,l]. We propose the first known algorithm for this problem in O(n) preprocessing time and O(1) time per query under the unit-cost RAM model. We also use the RMSQ techniques to solve three relevant problems in linear time. These variations on the basic theme demonstrate the utilities of the techniques developed in this paper.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bender, M.A., Farach-Colton, M.: The LCA Problem Revisited. In: Proceedings of the 4th Latin American Symposium on Theoretical Informatics, vol. 17, pp. 88–94 (2000)
Bentley, J.: Programming Pearls - Algorithm Design Techniques. In: CACM, pp. 865–871 (1984)
Chung, K., Lu, H.-I.: An optimal algorithm for the maximum-density segment problem. In: Di Battista, G., Zwick, U. (eds.) ESA 2003. LNCS, vol. 2832, pp. 136–147. Springer, Heidelberg (2003)
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)
Gabow, H., Bentley, J., Tarjan, R.:Scaling and Related Techniques for Geometry Problems. In: Proc. Symp Theory of Computing(STOC), pp. 135–143 (1984)
Gusfield, D.: Algorithms on Strings, Trees, and Sequences: Computer Science and Computational Biology. Cambridge University Press, Cambridge (1999)
Harel, D., Tarjan, R.E.: Fast Algorithms for Finding Nearest Common Ancestors. SIAM J Comput. 13, 338–355 (1984)
Huang, X.: An Algorithm for Identifying Regions of a DNA Sequence that Satisfy a Content Requirement. CABIOS 10, 219–225 (1994)
Lin, Y.-L., Huang, X., Jiang, T., Chao, K.-M.: MAVG: Locating Non-Overlapping Maximum Average Segments in a Given Sequence. Bioinformatics 19, 151–152 (2003)
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, 570–586 (2002)
Ruzzo, W.L., Tompa, M.: A Linear Time Algorithm for Finding All Maximal Scoring Subsequences. In: 7th Intl. Conf. Intelligent Systems for Molecular Biology, Heidelberg, Germany, pp. 234–241 (1999)
Schieber, B., Vishkin, U.: On Finding Lowest Common Ancestors: Simplification and Parallelization. SIAM J. Comput. 17, 1253–1262 (1988)
Vuillemin, J.: A Unifying Look at Data Structures. CACM 23, 229–239 (1980)
Wang, L., Xu, Y.: SEGID:Identifying Interesting Segments in (Multiple) Sequence Alignments. Bioinformatics 19, 297–298 (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Chen, KY., Chao, KM. (2004). On the Range Maximum-Sum Segment Query Problem. In: Fleischer, R., Trippen, G. (eds) Algorithms and Computation. ISAAC 2004. Lecture Notes in Computer Science, vol 3341. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30551-4_27
Download citation
DOI: https://doi.org/10.1007/978-3-540-30551-4_27
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-24131-7
Online ISBN: 978-3-540-30551-4
eBook Packages: Computer ScienceComputer Science (R0)