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Non-overlapping indexing – cache obliviously. (English) Zbl 07286734
Navarro, Gonzalo (ed.) et al., 29th annual symposium on combinatorial pattern matching, CPM 2018, July 2–4, 2018, Qingdao, China. Wadern: Schloss Dagstuhl – Leibniz Zentrum für Informatik. LIPIcs – Leibniz Int. Proc. Inform. 105, Article 8, 9 p. (2018).
Summary: The non-overlapping indexing problem is defined as follows: pre-process a given text \(\mathsf{T}[1,n]\) of length \(n\) into a data structure such that whenever a pattern \(P[1,p]\) comes as an input, we can efficiently report the largest set of non-overlapping occurrences of \(P\) in \(\textsf{T}\). The best known solution is by H. Cohen and E. Porat [Lect. Notes Comput. Sci. 5878, 1044–1053 (2009; Zbl 1273.68097)]. Their index size is \(O(n)\) words and query time is optimal \(O(p+\mathsf{nocc})\), where nocc is the output size. We study this problem in the cache-oblivious model and present a new data structure of size \(O(n\log n)\) words. It can answer queries in optimal \(O(\frac{p}{B}+\log_B n+\frac{\mathsf{nocc}}{B})\) I/Os, where \(B\) is the block size.
For the entire collection see [Zbl 1390.68025].

68W32 Algorithms on strings
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