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Range LCP. (English) Zbl 1410.68414
Summary: In this paper, we define the Range LCP problem as follows. Preprocess a string \(S\), of length \(n\), to enable efficient solutions of the following query: Given \([i, j]\), \(0<i\leqslant j\leqslant n\), compute \(\max_{\ell,k \in [i..j]}\mathrm{LCP}(S_\ell,S_k)\), where \(\mathrm{LCP}(S_\ell, S_k)\) is the length of the longest common prefix of the suffixes of \(S\) starting at locations \(\ell\) and \(k\). This is a natural generalization of the classical LCP problem. We provide algorithms with the following complexities:
Preprocessing Time: \(O(|S|)\), Space: \(O(|S|)\), Query Time: \(O(|j-i|\log\log n)\).
Preprocessing Time: none, Space: \(O(|j-i|\log |j-i|)\), Query Time: \(O(|j-i|\log |j-i|)\). However, the query just gives the pairs with the longest LCP, not the LCP itself.
Preprocessing Time: \(O(|S| \log^2 |S|)\), Space: \(O(|S| \log^{1+\varepsilon}|S|)\) for arbitrary small constant \(\varepsilon\), Query Time: \(O(\log\log |S|)\).

68W32 Algorithms on strings
68P05 Data structures
68W40 Analysis of algorithms
Full Text: DOI
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