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Efficient algorithms for finding a longest common increasing subsequence

Author

Listed:
  • Wun-Tat Chan

    (University of Hong Kong)

  • Yong Zhang

    (University of Hong Kong)

  • Stanley P. Y. Fung

    (University of Leicester)

  • Deshi Ye

    (University of Hong Kong)

  • Hong Zhu

    (Fudan University)

Abstract

We study the problem of finding a longest common increasing subsequence (LCIS) of multiple sequences of numbers. The LCIS problem is a fundamental issue in various application areas, including the whole genome alignment. In this paper we give an efficient algorithm to find the LCIS of two sequences in $$O({\rm min}(r {\rm log} \ell, n \ell +r) {\rm log} {\rm log} n + Sort(n))$$ time where n is the length of each sequence andr is the number of ordered pairs of positions at which the two sequences match, ℓ is the length of the LCIS, and Sort(n) is the time to sort n numbers. For m sequences wherem ≥ 3, we find the LCIS in $$O({\rm min}(mr^2, r {\rm log}\ell {\rm log}^m r)+m\cdot $$ Sort(n)) time where r is the total number of m-tuples of positions at which the m sequences match. The previous results find the LCIS of two sequences in O(n 2) and $$O(n\ell {\rm log} {\rm log} n+$$ Sort(n)) time. Our algorithm is faster when r is relatively small, e.g., for $$r

Suggested Citation

  • Wun-Tat Chan & Yong Zhang & Stanley P. Y. Fung & Deshi Ye & Hong Zhu, 2007. "Efficient algorithms for finding a longest common increasing subsequence," Journal of Combinatorial Optimization, Springer, vol. 13(3), pages 277-288, April.
    • Handle: RePEc:spr:jcomop:v:13:y:2007:i:3:d:10.1007_s10878-006-9031-7
    DOI: 10.1007/s10878-006-9031-7
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    Cited by:

    1. Xiaozhou He & Yinfeng Xu, 2018. "The longest commonly positioned increasing subsequences problem," Journal of Combinatorial Optimization, Springer, vol. 35(2), pages 331-340, February.

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