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On Locating Disjoint Segments with Maximum Sum of Densities

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Abstract

Given a sequence A of n real numbers and two positive integers l and k, where \(k\leq \frac{n}{l}\) , we study the problem of locating k disjoint segments of A, each of length at least l, such that the sum of their densities is maximized. The best previously known algorithm, due to Bergkvist and Damaschke, runs in O(nl+k 2 l 2) time. In this paper, we propose an O(n+k 2 llog l)-time algorithm for it. We also give an optimal algorithm for a related problem raised by Lin et al. in 2003, where the goal is to locate k disjoint maximum-density segments in a given sequence.

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References

  1. Bergkvist, A., Damaschke, P.: Fast algorithms for finding disjoint subsequences with extremal densities. Pattern Recognit. 39(12), 2281–2292 (2006)

    Article  MATH  Google Scholar 

  2. Bernholt, T., Eisenbrand, F., Hofmeister, T.: A geometric framework for solving subsequence problems in computational biology efficiently. In: Proceedings of the 23rd Annual Symposium on Computational Geometry, pp. 310–318 (2007)

  3. Chen, Y.H., Lu, H.-I., Tang, C.Y.: Disjoint segments with maximum density. In: Proceedings of the 5th Annual International Conference on Computational Science, pp. 845–850 (2005)

  4. Chung, K.-M., Lu, H.-I.: An optimal algorithm for the maximum-density segment problem. SIAM J. Comput. 34(2), 373–387 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  5. Fukuda, T., Morimoto, Y., Morishita, S., Tokuyama, T.: Mining optimized association rules for numeric attributes. J. Comput. Syst. Sci. 58(1), 1–12 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  6. Goldwasser, M., Kao, M.-Y., Lu, H.-I.: Linear-time algorithms for computing maximum-density sequence segments with bioinformatics applications. J. Comput. Syst. Sci. 70(2), 128–144 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  7. Huang, X.: An algorithm for identifying regions of a DNA sequence that satisfy a content requirement. Comput. Appl. Biosci. 10(3), 219–225 (1994)

    Google Scholar 

  8. Kim, S.K.: A linear-time algorithm for finding a maximum-density segment of a sequence. Inform. Process. Lett. 86(6), 339–342 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  9. Lin, Y.-L., Huang, X., Jiang, T., Chao, K.-M.: MAVG: locating non-overlapping maximum average segments in a given sequence. Bioinformatics 19(1), 151–152 (2003)

    Article  Google Scholar 

  10. Lin, Y.-L., Jiang, T., Chao, K.-M.: Efficient algorithms for locating the length-constrained heaviest segments with applications to biomolecular sequence analysis. J. Comput. Syst. Sci. 65(3), 570–586 (2002)

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science and Information Engineering, National Taiwan University, Taipei, Taiwan, 106, Taiwan, Republic of China

    Hsiao-Fei Liu & Kun-Mao Chao

  2. Graduate Institute of Biomedical Electronics and Bioinformatics, National Taiwan University, Taipei, Taiwan, 106, Taiwan, Republic of China

    Kun-Mao Chao

  3. Graduate Institute of Networking and Multimedia, National Taiwan University, Taipei, Taiwan, 106, Taiwan, Republic of China

    Kun-Mao Chao

Authors
  1. Hsiao-Fei Liu
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  2. Kun-Mao Chao
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Corresponding author

Correspondence to Kun-Mao Chao.

Additional information

A preliminary version of this work appeared in Proceedings of the 17th International Symposium on Algorithms and Computation, India, 2006.

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Liu, HF., Chao, KM. On Locating Disjoint Segments with Maximum Sum of Densities. Algorithmica 54, 107–117 (2009). https://doi.org/10.1007/s00453-007-9122-6

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  • DOI: https://doi.org/10.1007/s00453-007-9122-6

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