Efficient algorithms for finding a longest common increasing subsequence

Authors:
Wun-Tat Chan;Yong Zhang;Stanley P. Y. Fung;Deshi Ye;Hong Zhu
Affiliations:
Department of Computer Science, University of Hong Kong, Hong Kong;,Department of Computer Science, University of Hong Kong, Hong Kong;Department of Computer Science, City University of Hong Kong, Hong Kong;Department of Computer Science, University of Hong Kong, Hong Kong;Department of Computer Science and Engineering, Fudan University, China
Venue:
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Year:
2005

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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 and pattern recognition. In this paper we give an efficient algorithm to find the LCIS of two sequences in O(min(r logℓ, nℓ+r)loglog n+n log n) time where n is the length of each sequence and r is the total number of ordered pairs of positions at which the two sequences match and ℓ is the length of the LCIS. For m sequences where m ≥ 3, we find the LCIS in O(min(mr2,mr log ℓlogmr)+mnlog 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(n2) and O(n ℓ log n) time. Our algorithm is faster when r is relatively small, e.g., for rn2/loglogn,nℓ).