2026-09-21T03:42:46Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:25557 2026-09-05T19:20:23Z ddc:004 open_access

Dynamic Pattern Matching with Wildcards Naeini, Arshia Ataee Mobed, Amir-Parsa Seddighin, Masoud Seddighin, Saeed pattern matching wildcards dynamic algorithms string algorithms data structures 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Arshia Ataee Naeini and Amir-Parsa Mobed and Masoud Seddighin and Saeed Seddighin 2026 Is Part Of LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.STACS.2026.68 urn:nbn:de:0030-drops-255579 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.68 eng https://creativecommons.org/licenses/by/4.0/legalcode