Book chapter · Conference paper
Time-Space Trade-offs for Longest Common Extensions
Department of Informatics and Mathematical Modeling, Technical University of Denmark1
Algorithms and Logic, Department of Informatics and Mathematical Modeling, Technical University of Denmark2
Computer Science and Engineering, Department of Informatics and Mathematical Modeling, Technical University of Denmark3
University of Warwick4
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.
Language: | English |
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Publisher: | Springer |
Year: | 2012 |
Pages: | 293-305 |
Proceedings: | 23rd Annual Symposium on Combinatorial Pattern Matchin |
Series: | Lecture Notes in Computer Science |
ISBN: | 3642312640 , 3642312659 , 9783642312649 and 9783642312656 |
ISSN: | 16113349 and 03029743 |
Types: | Book chapter and Conference paper |
DOI: | 10.1007/978-3-642-31265-6_24 |
ORCIDs: | Bille, Philip and Gortz, Inge Li |