Abstract
The compact suffix array (CSA) is a space-efficient full-text index, which is fast in practice to search for patterns in a static text. Compared to other compressed suffix arrays (Grossi and Vitter, Sadakane, Ferragina and Manzini), the CSA is significantly larger (2.7 times the text size, as opposed to 0.6–0.8 of compressed suffix arrays). The space of the CSA includes that of the text, which the CSA needs separately available. Compressed suffix arrays, on the other hand, include the text, that is, they are self-indexes. Although compressed suffix arrays are very fast to determine the number of occurrences of a pattern, they are in practice very slow to report even a few occurrence positions or text contexts. In this aspect the CSA is much faster. In this paper we contribute to this space-time trade off by introducing the Compressed CSA (CCSA), a self-index that improves the space usage of the CSA in exchange for search speed. We show that the occ occurrence positions of a pattern of length m in a text of length n can be reported in O((m+occ)log n) time using the CCSA, whose representation needs O(n(1+H k log n)) bits for any k, H k being the k-th order empirical entropy of the text. In practice the CCSA takes 1.6 times the text size (and includes the text). This is still larger than current compressed suffix arrays, and similar in size to the LZ-index of Navarro. Search times are by far better than for self-indexes that take less space than the text, and competitive against the LZ-index and versions of compressed suffix arrays tailored to take 1.6 times the text size.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Brodnik, A., Munro, I.: Membership in constant time and almost-minimum space. SIAM J. on Comp. 5, 1627–1640 (1999)
Burrows, M., Wheeler, D.J.: A block-sorting lossless data compression algorithm. DEC SRC Research Report 124 (1994)
Clark, D.: Compact Pat Trees. PhD thesis, University of Waterloo (1996)
Crochemore, M., Vérin, R.: Direct Construction of Compact Directed Acyclic Word Graphs. In: Hein, J., Apostolico, A. (eds.) CPM 1997. LNCS, vol. 1264, pp. 116–129. Springer, Heidelberg (1997)
Ferragina, P., Manzini, G.: Opportunistic Data Structures with Applications. In: Proc. IEEE Symp. on Foundations of Computer Science (FOCS 2000), pp. 390–398 (2000)
Ferragina, P., Manzini, G.: An Experimental Study of an Opportunistic Index. In: Proc. 12th Symposium on Discrete Algorithms (SODA 2001), pp. 269–278 (2001)
Giegerich, R., Kurtz, S., Stoye, J.: Efficient Implementation of Lazy Suffix Trees. In: Vitter, J.S., Zaroliagis, C.D. (eds.) WAE 1999. LNCS, vol. 1668, pp. 30–42. Springer, Heidelberg (1999)
Grossi, R., Vitter, J.: Compressed suffix arrays and suffix trees with applications to text indexing and string matching. In: Proc. 32nd Symposium on Theory of Computing (STOC 2000), pp. 397–406 (2000)
Harman, D.: Overview of the Third Text REtrieval Conference. In: Proc. TREC-3, pp. 1–19 (1995) ;NIST Special Publication pp. 500-207.
Jacobson, G.: Succinct Static Data Structures. PhD thesis, CMU-CS-89-112, Carnegie Mellon University (1989)
Manber, U., Myers, G.: Suffix arrays: A new method for on-line string searches. SIAM J. Comput. 22, 935–948 (1993)
Manzini, G.: An Analysis of the Burrows-Wheeler Transform. J. of the ACM 48(3), 407–430 (2001)
Munro, I.: Tables. In: Proc. FSTTCS 1996, pp. 37–42 (1996)
Mäkinen, V.: Compact Suffix Array — A Space-efficient Full-text Index. Fundamenta Informaticae 56(1-2), 191–210 (2003)
Mäkinen, V., Navarro, G.: New search algorithms and time/space trade offs for succinct suffix arrays. Technical report C-2004-20, Dept. of Computer Science, Univ. of Helsinki (April 2004)
Navarro, G.: Indexing text using the ziv-lempel trie. In: Laender, A.H.F., Oliveira, A.L. (eds.) SPIRE 2002. LNCS, vol. 2476, pp. 325–336. Springer, Heidelberg (2002) ;Extended version to appear in J. of Discrete Algorithms
Navarro, G.: The LZ-index: A Text Index Based on the Ziv-Lempel Trie. Technical Report TR/DCC-2003-1, Dept. of Computer Science, Univ. of Chile (January 2003)
Sadakane, K.: Compressed text databases with efficient query algorithms based on the compressed suffix array. In: Lee, D.T., Teng, S.-H. (eds.) ISAAC 2000. LNCS, vol. 1969, pp. 410–421. Springer, Heidelberg (2000)
Weiner, P.: Linear pattern matching algorithms.In: Proc. IEEE 14th Annual Symposium on Switching and Automata Theory, pp.1–11 (1973)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Mäkinen, V., Navarro, G. (2004). Compressed Compact Suffix Arrays. In: Sahinalp, S.C., Muthukrishnan, S., Dogrusoz, U. (eds) Combinatorial Pattern Matching. CPM 2004. Lecture Notes in Computer Science, vol 3109. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27801-6_32
Download citation
DOI: https://doi.org/10.1007/978-3-540-27801-6_32
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22341-2
Online ISBN: 978-3-540-27801-6
eBook Packages: Springer Book Archive