B. Nikolic, A. Kartelj, M. Djukanovic, M. Grbic, C. Blum, G. Raidl:

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

Mathematics,9(2021), 1 - 25.

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.

http://dx.doi.org/10.3390/math9131515

https://publik.tuwien.ac.at/files/publik_301813.pdf

Created from the Publication Database of the Vienna University of Technology.