## Time-Space Trade-offs for Longest Common Extensions

Publication: Research - peer-review › Article in proceedings – Annual report year: 2012

### Standard

**Time-Space Trade-offs for Longest Common Extensions.** / Bille, Philip; Gortz, Inge Li; Sach, Benjamin; Vildhoj, Hjalte Wedel.

Publication: Research - peer-review › Article in proceedings – Annual report year: 2012

### Harvard

*Combinatorial Pattern Matching.*Springer, pp. 293-305. Lecture Notes in Computer Science, vol. 7354, DOI: 10.1007/978-3-642-31265-6_24

### APA

*Combinatorial Pattern Matching.*(pp. 293-305). Springer. (Lecture Notes in Computer Science, Vol. 7354). DOI: 10.1007/978-3-642-31265-6_24

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### MLA

*Combinatorial Pattern Matching.*Springer. 2012. 293-305. (Lecture Notes in Computer Science, Volume 7354). Available: 10.1007/978-3-642-31265-6_24

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### Author

### Bibtex

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### RIS

TY - GEN

T1 - Time-Space Trade-offs for Longest Common Extensions

AU - Bille,Philip

AU - Gortz,Inge Li

AU - Sach,Benjamin

AU - Vildhoj,Hjalte Wedel

PY - 2012

Y1 - 2012

N2 - We revisit the longest common extension (LCE) problem, that is, preprocess a string T into a compact data structure that supports fast LCE queries. An LCE query takes a pair (i,j) of indices in T and returns the length of the longest common prefix of the suffixes of T starting at positions i and j. We study the time-space trade-offs for the problem, that is, the space used for the data structure vs. the worst-case time for answering an LCE query. Let n be the length of T. Given a parameter τ, 1 ≤ τ ≤ n, we show how to achieve either O(n/√τ) space and O(τ) query time, or O(n/τ) space and O(τ log(|LCE(i,j)|/τ)) query time, where |LCE(i,j)| denotes the length of the LCE returned by the query. These bounds provide the first smooth trade-offs for the LCE problem and almost match the previously known bounds at the extremes when τ = 1 or τ = n. We apply the result to obtain improved bounds for several applications where the LCE problem is the computational bottleneck, including approximate string matching and computing palindromes. Finally, we also present an efficient technique to reduce LCE queries on two strings to one string.

AB - We revisit the longest common extension (LCE) problem, that is, preprocess a string T into a compact data structure that supports fast LCE queries. An LCE query takes a pair (i,j) of indices in T and returns the length of the longest common prefix of the suffixes of T starting at positions i and j. We study the time-space trade-offs for the problem, that is, the space used for the data structure vs. the worst-case time for answering an LCE query. Let n be the length of T. Given a parameter τ, 1 ≤ τ ≤ n, we show how to achieve either O(n/√τ) space and O(τ) query time, or O(n/τ) space and O(τ log(|LCE(i,j)|/τ)) query time, where |LCE(i,j)| denotes the length of the LCE returned by the query. These bounds provide the first smooth trade-offs for the LCE problem and almost match the previously known bounds at the extremes when τ = 1 or τ = n. We apply the result to obtain improved bounds for several applications where the LCE problem is the computational bottleneck, including approximate string matching and computing palindromes. Finally, we also present an efficient technique to reduce LCE queries on two strings to one string.

U2 - 10.1007/978-3-642-31265-6_24

DO - 10.1007/978-3-642-31265-6_24

M3 - Article in proceedings

SN - 978-3-642-31264-9

SP - 293

EP - 305

BT - Combinatorial Pattern Matching

PB - Springer

ER -