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Multiplication Algorithms for Monge Matrices

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String Processing and Information Retrieval (SPIRE 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6393))

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Abstract

In this paper we study algorithms for the max-plus product of Monge matrices. These algorithms use the underlying regularities of the matrices to be faster than the general multiplication algorithm, hence saving time. A non-naive solution is to iterate the SMAWK algorithm. For specific classes there are more efficient algorithms. We present a new multiplication algorithm (MMT), that is efficient for general Monge matrices and also for specific classes. The theoretical and empirical analysis shows that MMT operates in near optimal space and time. Hence we give further insight into an open problem proposed by Landau. The resulting algorithms are relevant for bio-informatics, namely because Monge matrices occur in string alignment problems.

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References

  1. Burkard, R., Klinz, B., Rudolf, R.: Perspectives of Monge properties in optimization. Discrete Applied Mathematics 70(2), 95–161 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  2. Apostolico, A., Atallah, M.J., Larmore, L.L., McFaddin, S.: Efficient parallel algorithms for string editing and related problems. SIAM J. Comput. 19(5), 968–988 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  3. Schmidt, J.: All highest scoring paths in weighted grid graphs and their application to finding all approximate repeats in strings. SIAM Journal on Computing 27, 972 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  4. Tiskin, A.: Semi-local longest common subsequences in subquadratic time. J. Discrete Algorithms 6(4), 570–581 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  5. Landau, G., Myers, E., Schmidt, J.: Incremental string comparison. SIAM Journal on Computing 27, 557–582 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  6. Ishida, Y., Inenaga, S., Shinohara, A., Takeda, M.: Fully incremental LCS computation. In: Liśkiewicz, M., Reischuk, R. (eds.) FCT 2005. LNCS, vol. 3623, pp. 563–574. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  7. Alves, C.E.R., Cáceres, E.N., Song, S.W.: An all-substrings common subsequence algorithm. Discrete Applied Mathematics 156(7), 1025–1035 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  8. Landau, G.M.: Can dist tables be merged in linear time – An open problem. In: Proceedings of the Prague Stringology Conference 2006 (2006)

    Google Scholar 

  9. Tiskin, A.: Fast distance multiplication of unit-monge matrices. In: ACM-SIAM SODA, pp. 1287–1296 (2010)

    Google Scholar 

  10. Tiskin, A.: Semi-local string comparison: algorithmic techniques and applications. ArXiv e-prints (July 2007), arXiv0707.3619T

    Google Scholar 

  11. JáJá, J., Mortensen, C.W., Shi, Q.: Space-efficient and fast algorithms for multidimensional dominance reporting and counting. In: Fleischer, R., Trippen, G. (eds.) ISAAC 2004. LNCS, vol. 3341, pp. 558–568. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  12. Aggarwal, A., Klawe, M., Moran, S., Shor, P., Wilber, R.: Geometric applications of a matrix-searching algorithm. Algorithmica 2(1), 195–208 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  13. Iliopoulos, C.S., Mouchard, L., Rahman, M.S.: A new approach to pattern matching in degenerate DNA/RNA sequences and distributed pattern matching. Mathematics in Computer Science 1(4), 557–569 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  14. Grossi, R., Gupta, A., Vitter, J.S.: High-order entropy-compressed text indexes. In: SODA, 841–850 (2003)

    Google Scholar 

  15. Dayhoff, M.O., Schwartz, R.M., Orcutt, B.C.: A model of evolutionary change in proteins. Atlas of protein sequence and structure  5(suppl. 3), 345–351 (1978)

    Google Scholar 

  16. Crochemore, M., Landau, G., Ziv-Ukelson, M.: A subquadratic sequence alignment algorithm for unrestricted scoring matrices. SIAM Journal on Computing 32(6), 1654–1673 (2003)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. CITI / Departamento de Informática, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Quinta da Torre, 2829-516, Caparica, Portugal

    Luís M. S. Russo

  2. INESC-ID, Knowledge Discovery and Bioinformatics Group, R. Alves Redol, 9, 1000-029, Lisbon, Portugal

    Luís M. S. Russo

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  1. Luís M. S. Russo
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Editors and Affiliations

  1. School of Physics and Mathematics, Edificio "B", Universidad Michoacana, Ciudad Universitaria, 5800, Morelia, Mich., Mexico

    Edgar Chavez

  2. Dept. of Computer Science and Enginerring, University of California, 92521, Riverside, CA, USA

    Stefano Lonardi

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Russo, L.M.S. (2010). Multiplication Algorithms for Monge Matrices. In: Chavez, E., Lonardi, S. (eds) String Processing and Information Retrieval. SPIRE 2010. Lecture Notes in Computer Science, vol 6393. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16321-0_9

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  • DOI: https://doi.org/10.1007/978-3-642-16321-0_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-16320-3

  • Online ISBN: 978-3-642-16321-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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