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The fundamental question considered in algorithms on strings is that ofindexing, that is, preprocessing a given string for specific queries. By now wehave a number of efficient solutions for this problem when the queries ask foran exact occurrence of a given pattern $P$. However, practical applicationsmotivate the necessity of considering more complex queries, for exampleconcerning near occurrences of two patterns. Recently, Bille et al. [CPM 2021]introduced a variant of such queries, called gapped consecutive occurrences, inwhich 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 $q_2-q_1 \in [a,b]$. By their results, we cannot hope for avery efficient indexing structure for such queries, even if $a=0$ is fixed(although at the same time they provided a non-trivial upper bound). Motivatedby this, we focus on a text given as a straight-line program (SLP) and designan index taking space polynomial in the size of the grammar that answers suchqueries in time optimal up to polylog factors.

Compressed Indexing for Consecutive Occurrences