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Succinct indexes for reporting discriminating and generic words. (English) Zbl 1330.68055
Summary: We consider the problem of indexing a collection $$\mathcal{D}$$ of $$D$$ strings (documents) of total $$n$$ characters from an alphabet set of size $$\sigma$$, such that whenever a pattern $$P$$ (of $$p$$ characters) and an integer $$\tau \in [1, D]$$ come as a query, we can efficiently report all (i) maximal generic words and (ii) minimal discriminating words as defined below:
$$\bullet$$
maximal generic word is a maximal extension of $$P$$ occurring in at least $$\tau$$ documents.
$$\bullet$$
minimal discriminating word is a minimal extension of $$P$$ occurring in at most $$\tau$$ documents.
These problems were introduced by G. Kucherov et al. [Lect. Notes Comput. Sci. 7608, 307–317 (2012; Zbl 1330.68059)], they proposed indexes occupying $$O(n \log n)$$ bits with query times $$O(p + \mathrm{output})$$ and $$O(p + \log \log n + \mathrm{output})$$ for Problem (i) and Problem (ii) respectively. The query time for Problem (ii) is later improved to optimal $$O(p + \mathrm{output})$$ by P. Gawrychowski et al. [Lect. Notes Comput. Sci. 8214, 129–140 (2013; Zbl 1330.68058)]. In this paper, we describe succinct indexes of $$n \log \sigma + o(n \log \sigma) + O(n)$$ bits space with near-optimal query times i.e., $$O(p + \log \log n + \mathrm{output})$$ for both these problems.
##### MSC:
 68P15 Database theory 68P05 Data structures 68P20 Information storage and retrieval of data 68W32 Algorithms on strings
##### Keywords:
succinct indexes; string searching; range queries
Full Text:
##### References:
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