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DOI: 10.4230/LIPIcs.STACS.2026.68

Dynamic Pattern Matching with Wildcards

Authors: Arshia Ataee Naeini, Amir-Parsa Mobed, Masoud Seddighin, and Saeed Seddighin

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract

We study the fully dynamic pattern matching problem where the pattern may contain up to k wildcard symbols, each matching any symbol of the alphabet. Both the text and the pattern are subject to updates (insert, delete, change). We design an algorithm with 𝒪(n log² n) preprocessing and update/query time 𝒪̃(kn^{k/{k+1}} + k² log n). The bound is truly sublinear for a constant k, and sublinear when k = o(log n). We further complement our results with a conditional lower bound: assuming subquadratic preprocessing time, achieving truly sublinear update time for the case k = Ω(log n) would contradict the Strong Exponential Time Hypothesis (SETH). Finally, we develop sublinear algorithms for two special cases: - If the pattern contains w non-wildcard symbols, we give an algorithm with preprocessing time 𝒪(nw) and update time 𝒪(w + log n), which is truly sublinear whenever w is truly sublinear. - Using FFT technique combined with block decomposition, we design a deterministic truly sublinear algorithm with preprocessing time 𝒪(n^{1.8}) and update time 𝒪(n^{0.8} log n) for the case that there are at most two non-wildcards.

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Arshia Ataee Naeini, Amir-Parsa Mobed, Masoud Seddighin, and Saeed Seddighin. Dynamic Pattern Matching with Wildcards. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 68:1-68:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{naeini_et_al:LIPIcs.STACS.2026.68,
  author =	{Naeini, Arshia Ataee and Mobed, Amir-Parsa and Seddighin, Masoud and Seddighin, Saeed},
  title =	{{Dynamic Pattern Matching with Wildcards}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{68:1--68:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.68},
  URN =		{urn:nbn:de:0030-drops-255579},
  doi =		{10.4230/LIPIcs.STACS.2026.68},
  annote =	{Keywords: pattern matching, wildcards, dynamic algorithms, string algorithms, data structures}
}

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DOI: 10.4230/LIPIcs.ITCS.2022.115

3+ε Approximation of Tree Edit Distance in Truly Subquadratic Time

Authors: Masoud Seddighin and Saeed Seddighin

Published in: LIPIcs, Volume 215, 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)

Abstract

Tree edit distance is a well-known generalization of the edit distance problem to rooted trees. In this problem, the goal is to transform a rooted tree into another rooted tree via (i) node addition, (ii) node deletion, and (iii) node relabel. In this work, we give a truly subquadratic time algorithm that approximates tree edit distance within a factor 3+ε. Our result is obtained through a novel extension of a 3-step framework that approximates edit distance in truly subquadratic time. This framework has also been previously used to approximate longest common subsequence in subquadratic time.

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Masoud Seddighin and Saeed Seddighin. 3+ε Approximation of Tree Edit Distance in Truly Subquadratic Time. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 115:1-115:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{seddighin_et_al:LIPIcs.ITCS.2022.115,
  author =	{Seddighin, Masoud and Seddighin, Saeed},
  title =	{{3+\epsilon Approximation of Tree Edit Distance in Truly Subquadratic Time}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{115:1--115:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.115},
  URN =		{urn:nbn:de:0030-drops-157116},
  doi =		{10.4230/LIPIcs.ITCS.2022.115},
  annote =	{Keywords: tree edit distance, approximation, subquadratic, edit distance}
}

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Documents authored by Seddighin, Masoud

Dynamic Pattern Matching with Wildcards

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3+ε Approximation of Tree Edit Distance in Truly Subquadratic Time

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