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DOI: 10.4230/LIPIcs.CPM.2024.22
Subsequences with Generalised Gap Constraints: Upper and Lower Complexity Bounds

Authors: Florin Manea, Jonas Richardsen, and Markus L. Schmid

Published in: LIPIcs, Volume 296, 35th Annual Symposium on Combinatorial Pattern Matching (CPM 2024)

Abstract
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} ⊆ 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.
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Florin Manea, Jonas Richardsen, and Markus L. Schmid. Subsequences with Generalised Gap Constraints: Upper and Lower Complexity Bounds. In 35th Annual Symposium on Combinatorial Pattern Matching (CPM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 296, pp. 22:1-22:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{manea_et_al:LIPIcs.CPM.2024.22,
  author =	{Manea, Florin and Richardsen, Jonas and Schmid, Markus L.},
  title =	{{Subsequences with Generalised Gap Constraints: Upper and Lower Complexity Bounds}},
  booktitle =	{35th Annual Symposium on Combinatorial Pattern Matching (CPM 2024)},
  pages =	{22:1--22:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-326-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{296},
  editor =	{Inenaga, Shunsuke and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2024.22},
  URN =		{urn:nbn:de:0030-drops-201329},
  doi =		{10.4230/LIPIcs.CPM.2024.22},
  annote =	{Keywords: String algorithms, subsequences with gap constraints, pattern matching, fine-grained complexity, conditional lower bounds, parameterised complexity}
}
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