Deterministic Sub-Linear Space LCE Data Structures With Efficient Construction

Tanimura, Yuka; I, Tomohiro; Bannai, Hideo; Inenaga, Shunsuke; Puglisi, Simon J.; Takeda, Masayuki

doi:10.4230/LIPIcs.CPM.2016.1

File

LIPIcs.CPM.2016.1.pdf

Filesize: 0.5 MB
10 pages

Document Identifiers

DOI: 10.4230/LIPIcs.CPM.2016.1
URN: urn:nbn:de:0030-drops-60655

Author Details

Yuka Tanimura

Tomohiro I

Hideo Bannai

Shunsuke Inenaga

Simon J. Puglisi

Masayuki Takeda

Cite AsGet BibTex

Yuka Tanimura, Tomohiro I, Hideo Bannai, Shunsuke Inenaga, Simon J. Puglisi, and Masayuki Takeda. Deterministic Sub-Linear Space LCE Data Structures With Efficient Construction. In 27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 54, pp. 1:1-1:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
https://doi.org/10.4230/LIPIcs.CPM.2016.1

Abstract

Given a string S of n symbols, a longest common extension query LCE(i,j) asks for the length of the longest common prefix of the $i$th and $j$th suffixes of S. LCE queries have several important applications in string processing, perhaps most notably to suffix sorting. Recently, Bille et al. (J. Discrete Algorithms 25:42-50, 2014, Proc. CPM 2015:65-76) described several data structures for answering LCE queries that offers a space-time trade-off between data structure size and query time. In particular, for a parameter 1 <= tau <= n, their best deterministic solution is a data structure of size O(n/tau) which allows LCE queries to be answered in O(tau) time. However, the construction time for all deterministic versions of their data structure is quadratic in n. In this paper, we propose a deterministic solution that achieves a similar space-time trade-off of O(tau * min(log(tau),log(n/tau)) query time using O(n/tau) space, but significantly improve the construction time to O(n*tau).

Keywords

longest common extension
longest common prefix
sparse suffix array

Metrics

Access Statistics
Total Accesses (updated on a weekly basis)

0

PDF Downloads

0

Metadata Views

References

Michael A. Bender and Martin Farach-Colton. The LCA problem revisited. In Proc. Latin'00, pages 88-94, 2000.
Philip Bille, Inge Li Gørtz, Mathias Bæk Tejs Knudsen, Moshe Lewenstein, and Hjalte Wedel Vildhøj. Longest common extensions in sublinear space. In Proc. CPM 2015, pages 65-76, 2015.
Philip Bille, Inge Li Gørtz, Benjamin Sach, and Hjalte Wedel Vildhøj. Time-space trade-offs for longest common extensions. J. Discrete Algorithms, 25:42-50, 2014.
Dan Gusfield. Algorithms on Strings, Trees, and Sequences. Cambridge University Press, 1997.
Juha Kärkkäinen. Fast BWT in small space by blockwise suffix sorting. Theor. Comput. Sci., 387(3):249-257, 2007.
Juha Kärkkäinen, Dominik Kempa, and Simon J. Puglisi. Linear time Lempel-Ziv factorization: Simple, fast, small. In Proc. CPM'13, volume 7922 of Lecture Notes in Computer Science, pages 189-200. Springer, 2013.
Juha Kärkkäinen, Peter Sanders, and Stefan Burkhardt. Linear work suffix array construction. J. ACM, 53(6):918-936, 2006.
Juha Kärkkäinen and Esko Ukkonen. Sparse suffix trees. In Proc. COCOON'96, pages 219-230, 1996.
Toru Kasai, Gunho Lee, Hiroki Arimura, Setsuo Arikawa, and Kunsoo Park. Linear-time longest-common-prefix computation in suffix arrays and its applications. In Proc. CPM'01, pages 181-192, 2001.
Dong Kyue Kim, Jeong Seop Sim, Heejin Park, and Kunsoo Park. Linear-time construction of suffix arrays. In Proc. CPM'03, pages 186-199, 2003.
Pang Ko and Srinivas Aluru. Space efficient linear time construction of suffix arrays. In Proc. CPM'03, pages 200-210, 2003.
Udi Manber and Gene Myers. Suffix arrays: A new method for on-line string searches. SIAM J. Comput., 22(5):935-948, 1993.
Simon J. Puglisi and Andrew Turpin. Space-time tradeoffs for longest-common-prefix array computation. In Proc. ISAAC'08, volume 5369 of Lecture Notes in Computer Science, pages 124-135. Springer, 2008.