TY - GEN

T1 - Small-space LCE data structure with constant-time queries

AU - Tanimura, Yuka

AU - Nishimoto, Takaaki

AU - Bannai, Hideo

AU - Inenaga, Shunsuke

AU - Takeda, Masayuki

PY - 2017/11/1

Y1 - 2017/11/1

N2 - The longest common extension (LCE) problem is to preprocess a given string ω of length n so that the length of the longest common prefix between suffixes of ω that start at any two given positions is answered quickly. In this paper, we present a data structure of O(z2 + n/t ) words of space which answers LCE queries in O(1) time and can be built in O(n log δ) time, where 1 ≤ T ≤ √n is a parameter, z is the size of the Lempel-Ziv 77 factorization of ω and φ is the alphabet size. The proposed LCE data structure does not access the input string ω when answering queries, and thus w can be deleted after preprocessing. On top of this main result, we obtain further results using (variants of) our LCE data structure, which include the following: For highly repetitive strings where the z2 term is dominated by n/x, we obtain a constant-time and sub-linear space LCE query data structure. Even when the input string is not well compressible via Lempel-Ziv 77 factorization, we still can obtain a constant-time and sub-linear space LCE data structure for suitable and for φ ≤ 2o(log n). The time-space trade-off lower bounds for the LCE problem by Bille et al. [J. Discrete Algorithms, 25:42-50, 2014] and by Kosolobov [CoRR, abs/1611.02891, 2016] do not apply in some cases with our LCE data structure.

AB - The longest common extension (LCE) problem is to preprocess a given string ω of length n so that the length of the longest common prefix between suffixes of ω that start at any two given positions is answered quickly. In this paper, we present a data structure of O(z2 + n/t ) words of space which answers LCE queries in O(1) time and can be built in O(n log δ) time, where 1 ≤ T ≤ √n is a parameter, z is the size of the Lempel-Ziv 77 factorization of ω and φ is the alphabet size. The proposed LCE data structure does not access the input string ω when answering queries, and thus w can be deleted after preprocessing. On top of this main result, we obtain further results using (variants of) our LCE data structure, which include the following: For highly repetitive strings where the z2 term is dominated by n/x, we obtain a constant-time and sub-linear space LCE query data structure. Even when the input string is not well compressible via Lempel-Ziv 77 factorization, we still can obtain a constant-time and sub-linear space LCE data structure for suitable and for φ ≤ 2o(log n). The time-space trade-off lower bounds for the LCE problem by Bille et al. [J. Discrete Algorithms, 25:42-50, 2014] and by Kosolobov [CoRR, abs/1611.02891, 2016] do not apply in some cases with our LCE data structure.

UR - http://www.scopus.com/inward/record.url?scp=85038430729&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85038430729&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.MFCS.2017.10

DO - 10.4230/LIPIcs.MFCS.2017.10

M3 - Conference contribution

AN - SCOPUS:85038430729

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - 42nd International Symposium on Mathematical Foundations of Computer Science, MFCS 2017

A2 - Larsen, Kim G.

A2 - Raskin, Jean-Francois

A2 - Bodlaender, Hans L.

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

T2 - 42nd International Symposium on Mathematical Foundations of Computer Science, MFCS 2017

Y2 - 21 August 2017 through 25 August 2017

ER -