The longest common subsequence (LCS) problem and its variations have been studied deeply in past decades. In the constrained longest common subsequence (CLCS) problem, given three sequences A, B, and C of lengths m, n, and r, respectively, its goal is to find the LCS of A and B that C is a subsequence contained in the LCS answer. This thesis proposes an algorithm for obtaining the CLCS length based on the diagonal concept for finding the LCS length proposed by Nakatsu et al. Our algorithm can find the CLCS length more efficiently with O(rL(m − L)) time and O(mr) space, where L is the CLCS length. As the experimental results show, our CLCS algorithm outperforms the previously published algorithms.
Given two sequences S 1 , S 2 , and a constrained sequence C, a longest common subsequence of S 1 , S 2 with restriction to C is called a constrained longest common subsequence of S 1 and S 2 with C. At the same time, an optimal alignment of S 1 , S 2 with restriction to C is called a constrained pairwise sequence alignment of S 1 and S 2 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, S 1 , and S 2 , 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.
The discretely-scaled string indexing problem asks one to preprocess a given text string T , so that for a queried pattern P , the matched positions in T that P appears with some discrete scale can be reported efficiently.
Abstract-In this paper, we focus on the design of the faulttolerant routing algorithm for the (n, k)-star graph. We apply the idea of collecting the limited global information used for routing on the n-star graph to the (n, k)-star graph. First, we build the probabilistic safety vector (PSV) with modified cycle patterns. Then, our routing algorithm decides the fault-free routing path with the help of PSV. The performance is judged by the average length of routing paths. Compared with distance first search and safety level, we get the best performance in the simulations.
The (n, k)-star graph is a generalization of the n-star graph. It has better scalability than the n-star graph and holds some good properties compared with the hypercube. This paper focuses on the design of the fault-tolerant routing algorithm for the (n, k)-star graph. We adopt the idea of collecting the limited global information used for routing on the n-star graph to the (n, k)-star graph. In the preliminary version of this paper, we built the probabilistic safety vector (PSV) with modified cycle patterns and developed the routing algorithm to decide the fault-free routing path with the help of PSV. Afterwards, we observed that the routing performance of PSV gets worse as the percentage of fault nodes increases, especially it exceeds 25%. In order to improve the routing performance with more faulty nodes, an adaptive method of threshold assignment for the PSV is also proposed. The performance is judged by the average length of routing paths. Compared with distance first search and safety level, PSV with dynamic threshold gets the best performance in the simulations.
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