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Compressed Indexing for Consecutive Occurrences

Authors Paweł Gawrychowski, Garance Gourdel, Tatiana Starikovskaya, Teresa Anna Steiner

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Author Details

Paweł Gawrychowski
  • Institute of Computer Science, University of Wrocław, Poland
Garance Gourdel
  • DI/ENS, PSL Research University, IRISA Inria Rennes, France
Tatiana Starikovskaya
  • DI/ENS, PSL Research University, Paris, France
Teresa Anna Steiner
  • DTU Compute, Technical University of Denmark, Lyngby, Denmark

Funding

  • Gawrychowski, Paweł: Partially supported by the Bekker programme of the Polish National Agency for Academic Exchange (PPN/BEK/2020/1/00444) and the grant ANR-20-CE48-0001 from the French National Research Agency (ANR).
  • Gourdel, Garance: Partially supported by the grant ANR-20-CE48-0001 from the French National Research Agency (ANR).
  • Starikovskaya, Tatiana: Partially supported by the grant ANR-20-CE48-0001 from the French National Research Agency (ANR).
  • Steiner, Teresa Anna: Supported by a research grant (VIL51463) from VILLUM FONDEN.

Cite As Get BibTex

Paweł Gawrychowski, Garance Gourdel, Tatiana Starikovskaya, and Teresa Anna Steiner. Compressed Indexing for Consecutive Occurrences. In 34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 259, pp. 12:1-12:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.CPM.2023.12

Abstract

The fundamental question considered in algorithms on strings is that of indexing, that is, preprocessing a given string for specific queries. By now we have a number of efficient solutions for this problem when the queries ask for an exact occurrence of a given pattern P. However, practical applications motivate the necessity of considering more complex queries, for example concerning near occurrences of two patterns. Recently, Bille et al. [CPM 2021] introduced a variant of such queries, called gapped consecutive occurrences, in which a query consists of two patterns P₁ and P₂ and a range [a,b], and one must find all consecutive occurrences (q₁,q₂) of P₁ and P₂ such that q₂-q₁ ∈ [a,b]. By their results, we cannot hope for a very efficient indexing structure for such queries, even if a = 0 is fixed (although at the same time they provided a non-trivial upper bound). Motivated by this, we focus on a text given as a straight-line program (SLP) and design an index taking space polynomial in the size of the grammar that answers such queries in time optimal up to polylog factors.

Subject Classification

ACM Subject Classification
  • Theory of computation → Data compression
  • Theory of computation → Pattern matching
Keywords
  • Compressed indexing
  • two patterns
  • consecutive occurrences

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