A Diagonal-Based Algorithm for the Constrained Longest Common Subsequence Problem

Abstract

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.

An A⁎ search algorithm for the constrained longest common subsequence problem

“…This algorithm avoids corresponding redundant computations. To the best of our knowledge, the latest algorithm developed for the CLCS problem was proposed by Hung et al [18]. It is based on the diagonal approach for the LCS problem by Nakatsu et al [19].…”

“…• The algorithm by Hung et al [18] was shown to be one order of magnitude faster than the algorithm of Deorowicz. Speed differences are especially noticeable in the presence of a rather high similarity of the input strings (> 70%) or a rather low similarity (< 20%).…”

“…• Most of the benchmark instances used in [18,15] seem rather easy to solve. In fact, most of the compared algorithms were able to do so in a fraction of a second.…”

“…• The comparison of the two state-of-the-art algorithms from Hung et al and Deorowicz and Obstoj) in [18] was limited to instances with a large fixed alphabet size | | = 256. Although it was shown that the algorithm of Hung et al is an order of magnitude faster than the algorithm from [15] on these instances, the observed differences in running times may not be significant as they are mostly below 0.1 seconds.…”

“…This procedure ensures that at least one feasible CLCS solution exists for each benchmark instances. Unfortunately, none of the artificial benchmarks from [15] and [18] were provided to us, although the respective authors were contacted with this concern.…”