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• W2568227468 abstract "The longest common extension (LCE) of two indices in a string is the length of the longest identical substrings starting at these two indices. The LCE problem asks to preprocess a string into a compact data structure that supports fast LCE queries. In this paper we generalize the LCE problem to trees and suggest a few applications of LCE in trees to tries and XML databases. Given a labeled and rooted tree $$T$$ of size $$n$$ , the goal is to preprocess $$T$$ into a compact data structure that support the following LCE queries between subpaths and subtrees in $$T$$ . Let $$v_1$$ , $$v_2$$ , $$w_1$$ , and $$w_2$$ be nodes of $$T$$ such that $$w_1$$ and $$w_2$$ are descendants of $$v_1$$ and $$v_2$$ respectively. We present the first non-trivial bounds for supporting these queries. For $${mathrm {LCE}_{ PP }}$$ queries, we present a linear-space solution with $$O(log ^{*} n)$$ query time. For $${mathrm {LCE}_{ PT }}$$ queries, we present a linear-space solution with $$O((log log n)^{2})$$ query time, and complement this with a lower bound showing that any path-tree LCE structure of size $$O(n text {polylog}(n))$$ must necessarily use $${varOmega }(log log n)$$ time to answer queries. For $${mathrm {LCE}_{ TT }}$$ queries, we present a time-space trade-off, that given any parameter $$tau $$ , $$1 le tau le n$$ , leads to an $$O(ntau )$$ space and $$O(n/tau )$$ query-time solution. This is complemented with a reduction to the set intersection problem implying that a fast linear space solution is not likely to exist." @default.
• W2568227468 created "2017-01-13" @default.
• W2568227468 creator A5000569191 @default.
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• W2568227468 date "2015-01-01" @default.
• W2568227468 modified "2023-10-16" @default.
• W2568227468 title "Longest Common Extensions in Trees" @default.
• W2568227468 cites W1501342714 @default.
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• W2568227468 doi "https://doi.org/10.1007/978-3-319-19929-0_5" @default.
• W2568227468 hasPublicationYear "2015" @default.
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