Solving the Longest Common Subsequence Problem Concerning Non-Uniform Distributions of Letters in Input Strings

Abstract

The longest common subsequence (LCS) problem is a prominent NP–hard optimization problem where, given an arbitrary set of input strings, the aim is to find a longest subsequence, which is common to all input strings. This problem has a variety of applications in bioinformatics, molecular biology and file plagiarism checking, among others. All previous approaches from the literature are dedicated to solving LCS instances sampled from uniform or near-to-uniform probability distributions of letters in the input strings. In this paper, we introduce an approach that is able to effectively deal with more general cases, where the occurrence of letters in the input strings follows a non-uniform distribution such as a multinomial distribution. The proposed approach makes use of a time-restricted beam search, guided by a novel heuristic named Gmpsum. This heuristic combines two complementary scoring functions in the form of a convex combination. Furthermore, apart from the close-to-uniform benchmark sets from the related literature, we introduce three new benchmark sets that differ in terms of their statistical properties. One of these sets concerns a case study in the context of text analysis. We provide a comprehensive empirical evaluation in two distinctive settings: (1) short-time execution with fixed beam size in order to evaluate the guidance abilities of the compared search heuristics; and (2) long-time executions with fixed target duration times in order to obtain high-quality solutions. In both settings, the newly proposed approach performs comparably to state-of-the-art techniques in the context of close-to-uniform instances and outperforms state-of-the-art approaches for non-uniform instances.

Longest Common Subsequence: Tabular vs. Closed-Form Equation Computation of Subsequence Probability

“…We implemented our proposed methods, i.e., k analytic , GCoV, and the Hyper-heuristic (HH) of those methods. To evaluate our results, we have implemented the best short-run methods proposed in the LCS literature, including k guess [21], BS-Ex [22], and GMPSUM [25]. All methods here are implemented using the Python version 3.8 programming language.…”

“…6. As the results in Tables 2, 3, and 4 show some values of GMPSUM [25] are left empty, especially for lengthier strings. It is impossible for us to compute some values of GMPSUM.…”

“…Moreover, we use a hyper-heuristic that makes use of both mentioned methods. To the best of our knowledge, the methods BS-Ex [22] and GMPSUM [25] presented the best results on benchmark datasets. Thus, we compare our results with them in Tables 2, 3, 4, 5, and 6.…”

“…But, the authors' proposal has a low performance for correlated strings. Nikolic et al [25] presented the GMPSUM heuristic function, which consists of two different functions as follows. The first one (GM) is based on the computation of the geometric mean over the geometric variance of the remaining lengths of strings.…”

Spam Detection using Reference Text: A Preliminary Study for Spam Ground Truth Generation

“…LCS or longest common sub string can find out the common sub string between two sentences [28]. A simple approach checks each sub string of sequence 1 to see if it is also a sub-string of sequence 2.…”