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Communication Dans Un Congrès Année : 2023

Compressed Indexing for Consecutive Occurrences

Résumé

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.
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hal-04325233 , version 1 (05-12-2023)

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Paweł Gawrychowski, Garance Gourdel, Tatiana Starikovskaya, Teresa Anna Steiner. Compressed Indexing for Consecutive Occurrences. CPM 2023 - 34th Annual Symposium on Combinatorial Pattern Matching, Jun 2023, Paris, France. ⟨10.4230/LIPIcs.CPM.2023.12⟩. ⟨hal-04325233⟩
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