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• W2346750882 abstract "A Longest Common Extension (LCE) query on a text $T$ of length $N$ asks for the length of the longest common prefix of suffixes starting at given two positions. We show that the signature encoding $mathcal{G}$ of size $w = O(min(z log N log^* M, N))$ [Mehlhorn et al., Algorithmica 17(2):183-198, 1997] of $T$, which can be seen as a compressed representation of $T$, has a capability to support LCE queries in $O(log N + log ell log^* M)$ time, where $ell$ is the answer to the query, $z$ is the size of the Lempel-Ziv77 (LZ77) factorization of $T$, and $M geq 4N$ is an integer that can be handled in constant time under word RAM model. In compressed space, this is the fastest deterministic LCE data structure in many cases. Moreover, $mathcal{G}$ can be enhanced to support efficient update operations: After processing $mathcal{G}$ in $O(w f_{mathcal{A}})$ time, we can insert/delete any (sub)string of length $y$ into/from an arbitrary position of $T$ in $O((y+ log Nlog^* M) f_{mathcal{A}})$ time, where $f_{mathcal{A}} = O(min { frac{loglog M loglog w}{logloglog M}, sqrt{frac{log w}{loglog w}} })$. This yields the first fully dynamic LCE data structure. We also present efficient construction algorithms from various types of inputs: We can construct $mathcal{G}$ in $O(N f_{mathcal{A}})$ time from uncompressed string $T$; in $O(n loglog n log N log^* M)$ time from grammar-compressed string $T$ represented by a straight-line program of size $n$; and in $O(z f_{mathcal{A}} log N log^* M)$ time from LZ77-compressed string $T$ with $z$ factors. On top of the above contributions, we show several applications of our data structures which improve previous best known results on grammar-compressed string processing." @default.
• W2346750882 created "2016-06-24" @default.
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• W2346750882 date "2016-05-05" @default.
• W2346750882 modified "2023-09-27" @default.
• W2346750882 title "Fully dynamic data structure for LCE queries in compressed space" @default.
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