Compressed Indexing for Consecutive Occurrences
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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 P_1 and P_2 and a range [a,b], and one must find all consecutive occurrences (q_1,q_2) of P_1 and P_2 such that q_2-q_1 ∈ [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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