TY - GEN

T1 - Range LCP

AU - Amir, Amihood

AU - Apostolico, Alberto

AU - Landau, Gad M.

AU - Levy, Avivit

AU - Lewenstein, Moshe

AU - Porat, Ely

PY - 2011

Y1 - 2011

N2 - In this paper, we define the Range LCP problem as follows. Preprocess a string S, of length n, to enable efficient solutions of the following query: Given {i j}, 0 < i ≤ j ≤ n, compute max ℓ, kε{i,...,j} LCP(S ℓ, S k), where LCP(S ℓ, S k ) is the length of the longest common prefix of the suffixes of S starting at locations ℓ and k. This is a natural generalization of the classical LCP problem. Surprisingly, while it is known how to preprocess a string in linear time to enable LCP computation of two suffixes in constant time, this seems quite difficult in the Range LCP problem. It is trivial to answer such queries in time O(|j - i| 2) after a linear-time preprocessing and easy to show an O(1) query algorithm after an O(|S| 2) time preprocessing. We provide algorithms that solve the problem with the following complexities: 1. Preprocessing Time: O(|S|), Space: O(|S|), Query Time: O(|j - i|log log n). 2. Preprocessing Time: no preprocessing, Space: O(|j - i|log|j - i|), Query Time: O(|j - i|log|j - i|). However, the query just gives the pairs with the longest LCP, not the LCP itself. 3. Preprocessing Time: O(|S|log 2 |S|), Space: O(|S|log 1 + ε |S|) for arbitrary small constant ε, Query Time: O(log log |S|).

AB - In this paper, we define the Range LCP problem as follows. Preprocess a string S, of length n, to enable efficient solutions of the following query: Given {i j}, 0 < i ≤ j ≤ n, compute max ℓ, kε{i,...,j} LCP(S ℓ, S k), where LCP(S ℓ, S k ) is the length of the longest common prefix of the suffixes of S starting at locations ℓ and k. This is a natural generalization of the classical LCP problem. Surprisingly, while it is known how to preprocess a string in linear time to enable LCP computation of two suffixes in constant time, this seems quite difficult in the Range LCP problem. It is trivial to answer such queries in time O(|j - i| 2) after a linear-time preprocessing and easy to show an O(1) query algorithm after an O(|S| 2) time preprocessing. We provide algorithms that solve the problem with the following complexities: 1. Preprocessing Time: O(|S|), Space: O(|S|), Query Time: O(|j - i|log log n). 2. Preprocessing Time: no preprocessing, Space: O(|j - i|log|j - i|), Query Time: O(|j - i|log|j - i|). However, the query just gives the pairs with the longest LCP, not the LCP itself. 3. Preprocessing Time: O(|S|log 2 |S|), Space: O(|S|log 1 + ε |S|) for arbitrary small constant ε, Query Time: O(log log |S|).

UR - http://www.scopus.com/inward/record.url?scp=84055217015&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-25591-5_70

DO - 10.1007/978-3-642-25591-5_70

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AN - SCOPUS:84055217015

SN - 9783642255908

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 683

EP - 692

BT - Algorithms and Computation - 22nd International Symposium, ISAAC 2011, Proceedings

T2 - 22nd International Symposium on Algorithms and Computation, ISAAC 2011

Y2 - 5 December 2011 through 8 December 2011

ER -