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arXiv · 1504.02671

Longest Common Extensions in Sublinear Space

Philip Bille·Inge Li Gørtz·Mathias Bæk Tejs Knudsen·Moshe Lewenstein·Hjalte Wedel Vildhøj
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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 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 $O(n)$ space and $O(1)$ query time. In this paper we show that for any trade-off parameter $1 \leq \tau \leq n$, the problem can be solved in $O(\frac{n}{\tau})$ space and $O(\tau)$ query time. This significantly improves the previously best known time-space trade-offs, and almost matches the best known time-space product lower bound.

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Philip Bille, Inge Li Gørtz, Mathias Bæk Tejs Knudsen, Moshe Lewenstein, Hjalte Wedel Vildhøj. 2015-04-10. Longest Common Extensions in Sublinear Space. https://arxiv.org/abs/1504.02671

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