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Erschienen in:
2015 | OriginalPaper | Buchkapitel
Longest Common Extensions in Sublinear Space
verfasst von : Philip Bille, Inge Li Gørtz, Mathias Bæk Tejs Knudsen, Moshe Lewenstein, Hjalte Wedel Vildhøj
Erschienen in: Combinatorial Pattern Matching
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Abstract
The longest common extension problem (LCE problem) is to construct a data structure for an input string \(T\) of length \(n\) that supports \({\mathrm {LCE}}(i,j)\) queries. Such a query returns the length of the longest common prefix of the suffixes starting at positions \(i\) and \(j\) in \(T\). This classic problem has a well-known solution that uses \(\mathcal {O}(n)\) space and \(\mathcal {O}(1)\) query time. In this paper we show that for any trade-off parameter \(1 \le \tau \le n\), the problem can be solved in \(\mathcal {O}(\frac{n}{\tau })\) space and \(\mathcal {O}(\tau )\) query time. This significantly improves the previously best known time-space trade-offs, and almost matches the best known time-space product lower bound.