Abstract
A maximum(-sum) contiguous subsequence of a real-valued sequence is a contiguous subsequence with the maximum cumulative sum. A minimal maximum contiguous subsequence is a minimal contiguous subsequence among all maximum ones of the sequence. We have designed and implemented a domain-decomposed parallel algorithm on cluster systems with Message Passing Interface that finds all successive minimal maximum subsequences of a random sample sequence from a normal distribution with negative mean. Our study employs the theory of random walk to derive an approximate probabilistic length bound for minimal maximum subsequences in an appropriate probabilistic setting, which is incorporated in the algorithm to facilitate the concurrent computation of all minimal maximum subsequences in hosting processors. We also present a preliminary empirical study of the speedup and efficiency achieved by the parallel algorithm with synthetic random data.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Akl, S.G., Guenther, G.R.: Applications of Broadcasting with Selective Reduction to the Maximal Sum Subsegment Problem. International Journal of High Speed Computing 3(2), 107–119 (1991)
Alves, C.E.R., Cáceres, E.N., Song, S.W.: Finding All Maximal Contiguous Subsequences of a Sequence of Numbers in \(O (1)\) Communication Rounds. IEEE Transactions on Parallel and Distributed Systems 24(3), 724–733 (2013)
Dai, H.-K., Su, H.-C.: A parallel algorithm for finding all successive minimal maximum subsequences. In: Correa, J.R., Hevia, A., Kiwi, M. (eds.) LATIN 2006. LNCS, vol. 3887, pp. 337–348. Springer, Heidelberg (2006)
He, X., Huang, C.-H.: Communication Efficient BSP Algorithm for All Nearest Smaller Values Problem. Journal of Parallel and Distributed Computing 61(10), 1425–1438 (2001)
JáJá, J.: An Introduction to Parallel Algorithms. Addison-Wesley (1992)
Karlin, S., Brendel, V.: Chance and Statistical Significance in Protein and DNA Sequence Analysis. Science 257(5066), 39–49 (1992)
Lin, T.-C., Lee, D.T.: Randomized Algorithm for the Sum Selection Problem. Theoretical Computer Science 377(1–3), 151–156 (2007)
Ruzzo, W.L., Tompa, M.: A linear time algorithm for finding all maximal scoring subsequences. In: The Seventh International Conference on Intelligent Systems for Molecular Biology, pp. 234–241. International Society for Computational Biology (1999)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Dai, H.K., Wang, Z. (2015). A Parallel Algorithm for Finding All Minimal Maximum Subsequences via Random Walk. In: Dediu, AH., Formenti, E., MartÃn-Vide, C., Truthe, B. (eds) Language and Automata Theory and Applications. LATA 2015. Lecture Notes in Computer Science(), vol 8977. Springer, Cham. https://doi.org/10.1007/978-3-319-15579-1_10
Download citation
DOI: https://doi.org/10.1007/978-3-319-15579-1_10
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-15578-4
Online ISBN: 978-3-319-15579-1
eBook Packages: Computer ScienceComputer Science (R0)