Longest Common Subsequence with Gap Constraints

TL;DR

This paper introduces efficient algorithms for the longest common subsequence problem with gap constraints, extending previous work to handle variable gap bounds and bounded range scenarios.

Contribution

It provides novel algorithms for LCS with gap constraints, improving computational efficiency in these specialized settings.

Findings

Algorithms for LCS with variable gap bounds

Algorithms for LCS within bounded ranges

Enhanced computational efficiency over prior methods

Abstract

We consider the longest common subsequence problem in the context of subsequences with gap constraints. In particular, following Day et al. 2022, we consider the setting when the distance (i. e., the gap) between two consecutive symbols of the subsequence has to be between a lower and an upper bound (which may depend on the position of those symbols in the subsequence or on the symbols bordering the gap) as well as the case where the entire subsequence is found in a bounded range (defined by a single upper bound), considered by Kosche et al. 2022. In all these cases, we present effcient algorithms for determining the length of the longest common constrained subsequence between two given strings.