Kuo-Tsung Tseng

AN ALGORITHM AND APPLICATIONS TO SEQUENCE ALIGNMENT WITH WEIGHTED CONSTRAINTS

Given two sequences S1, S2, and a constrained sequence C, a longest common subsequence of S1, S2 with restriction to C is called a constrained longest common subsequence of S1 and S2 with C. At the same time, an optimal alignment of S1, S2 with restriction to C is called a constrained pairwise sequence alignment of S1 and S2 with C. Previous algorithms have shown that the constrained longest common subsequence problem is a special case of the constrained pairwise sequence alignment problem, and that both of them can be solved in O(rnm) time, where r, n, and m represent the lengths of C, S1, and S2, respectively. In this paper, we extend the definition of constrained pairwise sequence alignment to a more flexible version, called weighted constrained pairwise sequence alignment, in which some constraints might be ignored. We first give an O(rnm)-time algorithm for solving the weighted constrained pairwise sequence alignment problem, then show that our extension can be adopted to solve some constraint-related problems that cannot be solved by previous algorithms for the constrained longest common subsequence problem or the constrained pairwise sequence alignment problem. Therefore, in contrast to previous results, our extension is a new and suitable model for sequence analysis.

Efficient algorithms for finding interleaving relationship between sequences

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^2m), where m is the number of blocks. An improved O(n^2+nm^2) algorithm is further proposed for the same blocked problem.

Dynamic programming algorithms for the mosaic longest common subsequence problem

The longest common subsequence (LCS) problem can be used to measure the relationship between sequences. In general, the inputs of the LCS problem are two sequences. For finding the relationship between one sequence and a set of sequences, we cannot apply the traditional LCS algorithms immediately. In this paper, we define the mosaic LCS (MLCS) problem of finding a mosaic sequence C, composed of repeatable k sequences in source sequence set S, such that the LCS of C and the target sequence T is maximal. Based on the concept of break points in sequence T, we first propose a divide-and-conquer algorithm with O(n^2m|S|+n^3logk) time for solving this problem, where n and m are the length of T and the maximal length of sequences in S, respectively. Furthermore, an improved algorithm with O(n(m+k)|S|) time is proposed by applying an efficient preprocessing for the MLCS problem.

1-Fair Alternator Designs for the de Bruijn Network

In a 1-fair alternator of a network of concurrent processors, no processor executes the critical step twice when one or more other processors have not executed the critical step yet. In this paper, two algorithms are proposed to solve the coloring (1-fair alternator design) problem on the de Bruijn network. The first one uses 2 lceillog2 krceil +1 colors to color the k-ary de Bruijn graph with two digits, while the second one uses p + 1 only colors, where (lfloor(p-1)/2rfloor p-1 < k les lfloorp/2rfloor p. The second coloring method is optimal when k = lfloorp/2rfloor p. Furthermore, the extension of our coloring method can be applied to the k-ary de Bruijn graph with three or more digits

Near-Optimal Block Alignments

The optimal alignment of two given biosequences is mathematically optimal, but it may not be a biologically optimal one. To investigate more possible alignments with biological meaning, one can relax the scoring functions to get near-optimal alignments. Though the near optimal alignments increase the possibility of finding the correct alignment, they may confuse the biologists because the size of candidates is large. In this paper, we present the filter scheme for the near-optimal alignments. An easy method for tracing the near-optimal alignments and an algorithm for filtering those alignments are proposed. The time complexity of our algorithm is O(dmn) in the worst case, where d is the maximum distance between the near-optimal alignments and the optimal alignment, and m and n are the lengths of the input sequences, respectively.