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Optimal Structure for Prefix-Substring Queries

Authors Paweł Gawrychowski , Florin Manea , Jonas Richardsen

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LIPIcs.CPM.2026.7.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Pattern matching
Keywords
  • Border Tree
  • Prefix-Substring Query
  • Data Structures

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Abstract

The prefix-substring matching problem [Gu, Farach, and Beigel, SODA 1994] consists in preprocessing a string s of length n for the following queries: given a triple (i, j, k) ∈ {0, … , |s|}³ with 1 ≤ j ≤ k, representing a prefix s[1:i] and a substring s[j:k] of s, find the longest prefix of s that is a suffix of s[1:i]s[j:k]. This is an useful primitive in e.g. dynamic text indexing, compressed pattern matching, and pattern matching on block graphs. The border tree uses some basic periodicity properties to answer such queries in 𝒪(log n) time after 𝒪(n) time preprocessing of s. We design a linear-space structure that answers such queries in constant time after 𝒪(n) time preprocessing of s over a polynomial alphabet, which is worst-case optimal.

Cite As Get BibTex

Paweł Gawrychowski, Florin Manea, and Jonas Richardsen. Optimal Structure for Prefix-Substring Queries. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 7:1-7:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.CPM.2026.7

Author Details

Paweł Gawrychowski
  • Faculty of Mathematics and Computer Science, University of Wrocław, Poland
Florin Manea
  • Department of Informatics, University of Göttingen, Germany
Jonas Richardsen
  • Department of Informatics, University of Göttingen, Germany

Funding

Paweł Gawrychowski is partially supported by the Polish National Science Centre grant number 2023/51/B/ST6/01505. The work of Florin Manea and Jonas Richardsen was partly supported by the German Research Foundation (DFG) through the Heisenberg project 466789228 and the research project 562495345.

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