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Dynamic Pattern Matching with Wildcards

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

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LIPIcs.STACS.2026.68.pdf
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ACM Subject Classification
  • Theory of computation → Problems, reductions and completeness
Keywords
  • pattern matching
  • wildcards
  • dynamic algorithms
  • string algorithms
  • data structures

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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.

Cite As Get BibTex

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) https://doi.org/10.4230/LIPIcs.STACS.2026.68

Author Details

Arshia Ataee Naeini
  • University of Tehran, Iran
Amir-Parsa Mobed
  • University of Tehran, Iran
Masoud Seddighin
  • Tehran Institute for Advanced Studies (TeIAS), Iran
Saeed Seddighin
  • Independent Researcher, Chicago, USA

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