Subsequences With Generalised Gap Constraints: Upper and Lower Complexity Bounds
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914756940529664 |
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| author | Manea, Florin Richardsen, Jonas Schmid, Markus L. |
| author_facet | Manea, Florin Richardsen, Jonas Schmid, Markus L. |
| contents | For two strings u, v over some alphabet A, we investigate the problem of embedding u into w as a subsequence under the presence of generalised gap constraints. A generalised gap constraint is a triple (i, j, C_{i, j}), where 1 <= i < j <= |u| and C_{i, j} is a subset of A^*. Embedding u as a subsequence into v such that (i, j, C_{i, j}) is satisfied means that if u[i] and u[j] are mapped to v[k] and v[l], respectively, then the induced gap v[k + 1..l - 1] must be a string from C_{i, j}. This generalises the setting recently investigated in [Day et al., ISAAC 2022], where only gap constraints of the form C_{i, i + 1} are considered, as well as the setting from [Kosche et al., RP 2022], where only gap constraints of the form C_{1, |u|} are considered.
We show that subsequence matching under generalised gap constraints is NP-hard, and we complement this general lower bound with a thorough (parameterised) complexity analysis. Moreover, we identify several efficiently solvable subclasses that result from restricting the interval structure induced by the generalised gap constraints. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_10497 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Subsequences With Generalised Gap Constraints: Upper and Lower Complexity Bounds Manea, Florin Richardsen, Jonas Schmid, Markus L. Data Structures and Algorithms For two strings u, v over some alphabet A, we investigate the problem of embedding u into w as a subsequence under the presence of generalised gap constraints. A generalised gap constraint is a triple (i, j, C_{i, j}), where 1 <= i < j <= |u| and C_{i, j} is a subset of A^*. Embedding u as a subsequence into v such that (i, j, C_{i, j}) is satisfied means that if u[i] and u[j] are mapped to v[k] and v[l], respectively, then the induced gap v[k + 1..l - 1] must be a string from C_{i, j}. This generalises the setting recently investigated in [Day et al., ISAAC 2022], where only gap constraints of the form C_{i, i + 1} are considered, as well as the setting from [Kosche et al., RP 2022], where only gap constraints of the form C_{1, |u|} are considered. We show that subsequence matching under generalised gap constraints is NP-hard, and we complement this general lower bound with a thorough (parameterised) complexity analysis. Moreover, we identify several efficiently solvable subclasses that result from restricting the interval structure induced by the generalised gap constraints. |
| title | Subsequences With Generalised Gap Constraints: Upper and Lower Complexity Bounds |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2404.10497 |