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Text Indexing: From Reporting to Counting

Authors Ben Bals , Panagiotis Charalampopoulos , Oded Lachish , Solon P. Pissis , Hilde Verbeek

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ACM Subject Classification
  • Theory of computation → Pattern matching
Keywords
  • text indexing
  • data structures
  • string algorithms
  • string processing

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Abstract

We prove an elementary yet powerful combinatorial lemma: in any rooted tree with L leaves, the number of nodes whose depth is smaller than the number of their leaf descendants is at most L. For any string T of length n, a direct application of this lemma to the suffix trie of T yields that the number of substrings of T whose length is smaller than their number of occurrences in T is at most n. This combinatorial insight leads to space-efficient data structures with optimal query times for string counting problems via the following algorithmic framework: store the counts for the at most n "frequent" substrings of T in a preprocessing step, and use a reporting query to count for the "infrequent" substrings. Our framework acts as a convenient black box, lifting indexes with reporting time 𝒪(|P|+|Occ_T(P)|) to support counting queries in time 𝒪(|P|), where P is the queried pattern and Occ_T(P) is the set of occurrences of P in T. As applications, we show efficient indexes for consecutive occurrences, weighted sequences, strings with utilities, and non-overlapping occurrences.

Cite As Get BibTex

Ben Bals, Panagiotis Charalampopoulos, Oded Lachish, Solon P. Pissis, and Hilde Verbeek. Text Indexing: From Reporting to Counting. In 34th Annual European Symposium on Algorithms (ESA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 388, pp. 68:1-68:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ESA.2026.68

Author Details

Ben Bals
  • CWI, Amsterdam, The Netherlands
  • Vrije Universiteit Amsterdam, The Netherlands
Panagiotis Charalampopoulos
  • King’s College London, UK
Oded Lachish
  • Birkbeck, University of London, UK
Solon P. Pissis
  • The Cyprus Institute, Nicosia, Cyprus
Hilde Verbeek
  • CWI, Amsterdam, The Netherlands

Funding

  • Verbeek, Hilde: Supported by a Constance van Eeden Fellowship.

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