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Constrained pairwise and center-star sequences alignment problems

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Abstract

Sequence alignment is a fundamental problem in computational biology, which is also important in theoretical computer science. In this paper, we consider the problem of aligning a set of sequences subject to a given constrained sequence. Given two sequences \(A=a_1a_2\ldots a_n\) and \(B=b_1b_2\ldots b_n\) with a given distance function and a constrained sequence \(C=c_1c_2\ldots c_k\), our goal is to find the optimal sequence alignment of A and B w.r.t. the constraint C. We investigate several variants of this problem. If \(C=c^k\), i.e., all characters in C are same, the optimal constrained pairwise sequence alignment can be solved in \(O(\min \{kn^2,(t-k)n^2\})\) time, where t is the minimum number of occurrences of character c in A and B. If in the final alignment, the alignment score between any two consecutive constrained characters is upper bounded by some value, which is called GB-CPSA, we give a dynamic programming with the time complexity \(O(kn^4/\log n)\). For the constrained center-star sequence alignment (CCSA), we prove that it is NP-hard to achieve the optimal alignment even over the binary alphabet. Furthermore, we show a negative result for CCSA, i.e., there is no polynomial-time algorithm to approximate the CCSA within any constant ratio.

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Acknowledgments

The authors thank the anonymous referees for their helpful comments to improve the presentation of this paper. This work was supported by NSFC (61433012, U1435215, 11171086), HK RGC Grant (HKU 7114/13E, HKU 7164/12E, HKU 7111/12E), HKU small project funding 201309176064, Natural Science Foundation of Hebei A2013201218, Chinese Academy of Sciences research Grant (No. KGZD-EW-103-5(9)), Fundamental Research Foundation of Northwestern Polytechnical University in China (Grant No. JC201164), Fundamental Research Funds for the Central Universities (Grant No. 3102015ZY081), and China Postdoctoral Science Foundation (Grant No. 2012M521803).

Author information

Authors and Affiliations

  1. Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China

    Yong Zhang

  2. College of International Education, Hong Kong Baptist University, Kowloon, Hong Kong, China

    Joseph Wun-Tat Chan

  3. Department of Computer Science, The University of Hong Kong, Pok Fu Lam, Hong Kong, China

    Yong Zhang, Francis Y. L. Chin & Hing-Fung Ting

  4. College of Computer Science, Zhejiang University, Hangzhou, China

    Deshi Ye

  5. College of Mathematics and Information Science, Hebei University, Baoding, China

    Feng Zhang

  6. School of Life Science, Northwestern Polytechnical University, Xi’an, China

    Jianyu Shi

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  1. Yong Zhang
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  2. Joseph Wun-Tat Chan
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  3. Francis Y. L. Chin
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  4. Hing-Fung Ting
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  5. Deshi Ye
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  6. Feng Zhang
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  7. Jianyu Shi
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Corresponding author

Correspondence to Deshi Ye.

Additional information

A preliminary version of this paper appeared in the Proceedings of the 8th International Frontiers of Algorithmics Workshop (FAW 2014) Lecture Notes in Computer Science, Volume 8497, 2014, pp 309–319.

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Zhang, Y., Chan, J.WT., Chin, F.Y.L. et al. Constrained pairwise and center-star sequences alignment problems. J Comb Optim 32, 79–94 (2016). https://doi.org/10.1007/s10878-015-9914-6

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  • DOI: https://doi.org/10.1007/s10878-015-9914-6

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