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A Parallel Algorithm for Finding All Successive Minimal Maximum Subsequences

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LATIN 2006: Theoretical Informatics (LATIN 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3887))

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Abstract

Efficient algorithms for finding multiple contiguous subsequences of a real-valued sequence having large cumulative sums, in addition to its combinatorial appeal, have widely varying applications such as in textual information retrieval and bioinformatics. A maximum 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 (with respect to subsequential containment) among all maximum ones of the sequence. We present a logarithmic-time and optimal linear-work parallel algorithm on the parallel random access machine model that finds all successive minimal maximum subsequences of a real-valued sequence.

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References

  1. 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)

    Article  MATH  Google Scholar 

  2. Berkman, O., Breslauer, D., Galil, Z., Schieber, B., Vishkin, U.: Highlyparallelizable problems. In: Proceedings of the 21st Annual ACM Symposium on Theory of Computing, pp. 309–319. Association for Computing Machinery (1989)

    Google Scholar 

  3. Brendel, V., Bucher, P., Nourbakhsh, I.R., Blaisdell, B.E., Karlin, S.: Methods and algorithms for statistical analysis of protein sequences. Proceedings of the National Academy of Sciences U.S.A. 89(6), 2002–2006 (1992)

    Article  Google Scholar 

  4. Chen, D.Z.: Efficient geometric algorithms on the EREW PRAM. IEEE Transactions on Parallel and Distributed Systems 6(1), 41–47 (1995)

    Article  Google Scholar 

  5. Gusfield, D.: Algorithms on Strings, Trees, and Sequences: Computer Science and Computational Biology. Cambridge University Press, New York (1997)

    Book  MATH  Google Scholar 

  6. JáJá, J.: An Introduction to Parallel Algorithms. Addison-Wesley, Reading (1992)

    MATH  Google Scholar 

  7. Karlin, S., Altschul, S.F.: Methods for assessing the statistical significance of molecular sequence features by using general scoring schemes. Proceedings of the National Academy of Sciences U.S.A. 87(6), 2264–2268 (1990)

    Article  MATH  Google Scholar 

  8. Karlin, S., Altschul, S.F.: Applications and statistics for multiple high-scoring segments in molecular sequences. Proceedings of the National Academy of Sciences U.S.A. 90(12), 5873–5877 (1993)

    Article  Google Scholar 

  9. Karlin, S., Brendel, V.: Chance and statistical significance in protein and DNA sequence analysis. Science 257(5066), 39–49 (1992)

    Article  Google Scholar 

  10. Karlin, S., Dembo, A.: Limit distributions of maximal segmental score among Markov-dependent partial sums. Advances in Applied Probability 24, 113–140 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  11. Ladner, R.E., Fischer, M.J.: Parallel prefix computation. Journal of the Association for Computing Machinery 27(4), 831–838 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  12. Ruzzo, W.L., Tompa, M.: A linear time algorithm for finding all maximal scoring subsequences. In: Proceedings of the Seventh International Conference on Intelligent Systems for Molecular Biology, pp. 234–241. International Society for Computational Biology (1999)

    Google Scholar 

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© 2006 Springer-Verlag Berlin Heidelberg

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Dai, HK., Su, HC. (2006). A Parallel Algorithm for Finding All Successive Minimal Maximum Subsequences. In: Correa, J.R., Hevia, A., Kiwi, M. (eds) LATIN 2006: Theoretical Informatics. LATIN 2006. Lecture Notes in Computer Science, vol 3887. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11682462_33

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  • DOI: https://doi.org/10.1007/11682462_33

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-32755-4

  • Online ISBN: 978-3-540-32756-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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