Efficient algorithms for finding interleaving relationship between sequences

• Published in: Information processing letters Vol. 105; no. 5; pp. 188 - 193
• Main Authors: Huang, Kuo-Si, Yang, Chang-Biau, Tseng, Kuo-Tsung, Ann, Hsing-Yen, Peng, Yung-Hsing
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 29.02.2008; Elsevier Science; Elsevier Sequoia S.A
• Subjects: Algorithmics. Computability. Computer arithmetics; Algorithms; Applied sciences; Artificial intelligence; Bioinformatics; Combinatorics; Combinatorics. Ordered structures; Computer science; control theory; systems; Correlation analysis; Design of algorithms; Designs and configurations; Dynamic programming; Exact sciences and technology; Genomics; Longest common subsequence; Mathematical models; Mathematics; Merged sequence; Miscellaneous; Problem solving; Problem solving, game playing; Sciences and techniques of general use; Studies; Theoretical computing; Dynamic programming; Design of algorithms; Bioinformatics; Longest common subsequence; Merged sequence; Measurement; Duplication; Computer theory; Solving; Merging; Sequence alignment; Research; Algorithm; Dynamics; Algorithm complexity; Information processing; Problem solving; Genome; Time complexity; Algorithm analysis
• ISSN: 0020-0190; 1872-6119
• DOI: 10.1016/j.ipl.2007.08.028

The longest common subsequence and sequence alignment problems have been studied extensively and they can be regarded as the relationship measurement between sequences. However, most of them treat sequences evenly or consider only two sequences. Recently, with the rise of whole-genome duplication research, the doubly conserved synteny relationship among three sequences should be considered. It is a brand new model to find a merging way for understanding the interleaving relationship of sequences. Here, we define the merged LCS problem for measuring the interleaving relationship among three sequences. An O ( n 3 ) algorithm is first proposed for solving the problem, where n is the sequence length. We further discuss the variant version of this problem with the block information. For the blocked merged LCS problem, we propose an algorithm with time complexity O ( n 2 m ) , where m is the number of blocks. An improved O ( n 2 + n m 2 ) algorithm is further proposed for the same blocked problem.