The Community for Technology Leaders
RSS Icon
Issue No.04 - April (2013 vol.24)
pp: 724-733
C. E. R. Alves , Univ. Sao Judas Tadeu, Sao Paulo, Brazil
E. N. Caceres , Fac. de Comput., Univ. Fed. do Mato Grosso do Sul, Campo Grande, Brazil
Siang Wun Song , Univ. of Sao Paulo, Sao Paulo, Brazil
Given a sequence A of real numbers, we wish to find a list of all nonoverlapping contiguous subsequences of A that are maximal. A maximal subsequence M of A has the property that no proper subsequence of M has a greater sum of values. Furthermore, M may not be contained properly within any subsequence of A with this property. This problem has several applications in Computational Biology and can be solved sequentially in linear time. We present a BSP/CGM algorithm that solves this problem using p processors in O(|A|=p) time and O(|A|=p) space per processor. The algorithm uses a constant number of communication rounds of size at most O(|A|=p). Thus, the algorithm achieves linear speedup and is highly scalable. To our knowledge, there are no previous known parallel BSP/CGM algorithms to solve this problem.
Parallel algorithms, Algorithm design and analysis, Program processors, Computational modeling, Materials, Amino acids, Multiprocessor interconnection, communication rounds, All maximal subsequences problem, maximum subsequence problem, parallel algorithm, coarse-grained multicomputer
C. E. R. Alves, E. N. Caceres, Siang Wun Song, "Finding All Maximal Contiguous Subsequences of a Sequence of Numbers in O(1) Communication Rounds", IEEE Transactions on Parallel & Distributed Systems, vol.24, no. 4, pp. 724-733, April 2013, doi:10.1109/TPDS.2012.149
[1] J. Bentleyd, Programming Pearls. Addison-Wesley, 1986.
[2] W.L. Ruzzo, and M. Tompa, "A Linear Time Algorithm for Finding All Maximal Scoring Subsequences," Proc. Seventh Int'l Conf. Intelligent Systems for Molecular Biology, pp. 234-241, 1999.
[3] S. Karlin and V. Brendel, "Chance and Significance in Protein and DNA Sequence Analysis," Science, vol. 257, pp. 39-49, 1992.
[4] M. Csuros, "Algorithms for Finding Maximal-Scoring Segment Sets," Proc. Fourth Workshop Algorithms in Bioinformatics (WABI '04), pp. 62-73, 2004.
[5] J.V. Braun and H.G. Muller, "Statistical Methods for DNA Sequence Segmentation," Statistical Science, vol. 13, pp. 142-162, 1998.
[6] Y.X. Fu and R.N. Curnow, "Maximum Likelihood Estimation of Multiple Change Points," Biometrika, vol. 77, pp. 563-573, 1990.
[7] W. Li, P. Bernaola-Galván, F. Haghighi, and I. Grosse, "Applications of Recursive Segmentation to the Analysis of DNA Sequences," Computer and Chemistry, vol. 26, pp. 491-510, 2002.
[8] R.J. Klein, Z. Misulovin, and S.R. Eddy, "Noncoding RNA Genes Identified in AT-Rich Hyperthermophiles," Proc. Nat'l Academy of Sciences of USA, vol. 99, pp. 7542-7547, 2002.
[9] J. Pasternack and D. Roth, "Extracting Article Text from the Web with Maximum Subsequence Segmentation," Proc. 18th Int'l Conf. World Wide Web, pp. 971-980, 2009.
[10] J.L. Bates and R.L. Constable, "Proofs as Programs," ACM Trans. Programming Languages and Systems, vol. 7, pp. 113-136, 1985.
[11] Z. Wen, "Fast Parallel Algorithm for the Maximum Sum Problem," Parallel Computing, vol. 21, pp. 461-466, 1995.
[12] K. Perumalla and N. Deo, "Parallel Algorithms for Maximum Subsequence and Maximum Subarray," Parallel Processing Letters, vol. 5, pp. 367-373, 1995.
[13] K. Qiu and S.G. Akl, "Parallel Maximum Sum Algorithms on Interconnection Networks," Technical Report Nos. 99-431, Dept. of Computer and Information Science, Queen's Univ., 1999.
[14] C.E.R. Alves, E.N. Cáceres, and S.W. Song, "BSP/CGM Algorithms for Maximum Subsequence and Maximum Subarray," Proc. 11th European PVM/MPIUsers' Group Meeting, P.K.J. Dongarra and D. Kranzlmuller, eds., pp. 139-146, 2004.
[15] H.-K. Dai and H.-C. Su, "A Parallel Algorithm for Finding All Successive Minimal Maximum Subsequences," Proc. Latin Am. Theoretical Informatics Symp. (LATIN '06), pp. 337-348, 2006.
[16] K.-Y. Chen and K.-M. Chao, "On the Range Maximum-Sum Segment Query Problem," Discrete Applied Math., vol. 155, pp. 2043-2052, 2007.
[17] C.E.R. Alves, E.N. Cáceres, and S.W. Song, "A BSP/CGM Algorithm for Finding All Maximal Contiguous Subsequences of a Sequence of Numbers," Proc. Int'l Conf. Parallel Processing (Euro-Par '06), W.E. Nagel, W.V. Walter, and W. Lehner, eds., pp. 831-840, 2006.
[18] L.G. Valiant, "General Purpose Parallel Architectures," Handbook of Theoretical Computer Science, J. van Leeuwen, ed., pp. 943-972, MIT Press/Elsevier, 1990.
[19] L. Valiant, "A Bridging Model for Parallel Computation," Comm. ACM, vol. 33, pp. 103-111, 1990.
[20] F. Dehne, X. Deng, P. Dymond, A. Fabri, and A.A. Kokhar, "A Randomized Parallel 3D Convex Hull Algorithm for Coarse Grained Multicomputers," Proc. ACM Symp. Parallel Algorithms and Architectures (SPAA '95), pp. 27-33, 1995.
[21] F. Dehne, A. Fabri, and A. Rau-Chaplin, "Scalable Parallel Geometric Algorithms for Coarse Grained Multicomputers," Proc. ACM Ninth Ann. Computational Geometry, pp. 298-307, 1993.
[22] E.L.G. Saukas and S.W. Song, "A Note on Parallel Selection on Coarse Grained Multicomputers," Algorithmica, vol. 24, pp. 371-380, 1999.
34 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool