an:06492067
Zbl 1330.68055
Biswas, Sudip; Patil, Manish; Shah, Rahul; Thankachan, Sharma V.
Succinct indexes for reporting discriminating and generic words
EN
Theor. Comput. Sci. 593, 165-173 (2015).
00348676
2015
j
68P15 68P05 68P20 68W32
succinct indexes; string searching; range queries
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) \textit{maximal generic words} and (ii) \textit{minimal discriminating words} as defined below:{\parindent=0,6cm \begin{itemize}\item[{\(\bullet\)}] maximal generic word is a maximal extension of \( P\) occurring in at least \(\tau\) documents. \item[{\(\bullet\)}] minimal discriminating word is a minimal extension of \(P\) occurring in at most \(\tau\) documents.
\end{itemize}} These problems were introduced by \textit{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 \textit{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.
Zbl 1330.68059; Zbl 1330.68058