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We consider the longest common subsequence problem in the context ofsubsequences with gap constraints. In particular, following Day et al. 2022, weconsider the setting when the distance (i. e., the gap) between two consecutivesymbols of the subsequence has to be between a lower and an upper bound (whichmay depend on the position of those symbols in the subsequence or on thesymbols bordering the gap) as well as the case where the entire subsequence isfound in a bounded range (defined by a single upper bound), considered byKosche et al. 2022. In all these cases, we present effcient algorithms fordetermining the length of the longest common constrained subsequence betweentwo given strings.

Longest Common Subsequence with Gap Constraints