Abstract
In this paper, we first consider some properties of strings who have the same suffix array. Next, we design a data structure to support rank and select operations on an alphabet Σ using nlog|Σ| + (n log|Σ|) bits in O(log|Σ|) time for a text of length n. It also supports an extended rank, namely rank ≤ , such that rank \(^{\rm \leq}_{\alpha}\)(T,i) returns the number of letters which are smaller than α in string T, plus the number of αs up to position i. Also, it runs in O(log|Σ|) time. By this structure, we implement the DAWG succinctly. The main structure only takes nlog|Σ| + o(nlog|Σ|) bits and supports basic operations of DAWG efficiently.
Supported by NSF of China No.60473099 and Foundation of Young Scientist of Jilin Province No.20040119.
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References
Abouelhoda, M.I., Ohlebusch, E., Kurtz, S.: Optimal exact string matching based on suffix arrays. In: Laender, A.H.F., Oliveira, A.L. (eds.) SPIRE 2002. LNCS, vol. 2476, pp. 31–43. Springer, Heidelberg (2002)
Bannai, H., Inenaga, S., Shinohara, A., Takeda, M.: Inferring strings from graphs and arrays. In: Rovan, B., Vojtáš, P. (eds.) MFCS 2003. LNCS, vol. 2747, pp. 208–217. Springer, Heidelberg (2003)
Blumer, A., Blumer, J., Haussler, D., Ehrenfeucht, A., Chen, M.T., Seiferas, J.: The smallest automation recognizing the subwords of a text. Theoretical Computer Science 40, 31–55 (1985)
Burrows, M., Wheeler, D.J.: A block-sorting lossless data compression algorithm. DEC SRC Research Report 124 (1994)
Crochemore, M., Hancart, C.: Automata for matching patterns. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages. Linear Modeling: Background and Application, vol. 2(9), pp. 399–462. Springer, Heidelberg (1997)
Ferragina, P., Manzini, G.: Opportunistic data structures with applications. In: Proceedings of the 4lst Annual IEEE Symposium on Foundations of Computer Science (FOCS), pp. 390–398 (2000)
Gonnet, G., Baeza-Yates, R., Snider, T.: New indices for text: PAT trees and PAT arrays. In: Frakes, W., Baeza-Yates, R.A. (eds.) Information Retrieval: Algorithms and Data Structures, pp. 66–82. Prentice-Hall, Englewood Cliffs (1992)
Gusfield, D.: Algorithms on Strings Trees and Sequences. Cambridge University-Press, New York (1997)
Grossi, R., Vitter, J.: Compressed suffix arrays and suffix trees with applications to text indexing and string matching. In: Proceedings of the 32nd ACM Symposium on Theory of Computing, STOC (2000)
He, M., Ian Munro, J., Srinivasa Rao, S.: A categorization theorem on suffix arrays with applications to space efficient text indexes. In: SIAM Symposium on Discrete Algorithms (SODA), pp. 23–32 (2005)
Jacobson, G.: Succinct static data structures. Technical Report CMU-CS-89-112, Dept. of Computer Science, Carnegie-Mellon University (January 1989)
Manber, U., Myers, G.: Suffix arrays: A new method for on-line string searches. SIAM Journal on Computing 22, 935–948 (1993)
Munro, J.I., Raman, V.: Succinct Representation of Balanced Parentheses, Static Trees and Planar Graphs. In: Proc. 38th Annual IEEE Symp. on Foundations of Computer Science, October 1997, pp. 118–126 (1997)
Munro, J.I.: Tables. In: Proceedings of the 16th ray Conference on Foundations of Software Technology and Computer Science (FSTTCS 1996). LNCS, vol. 1180, pp. 37–42 (1996)
Sadakane, K.: Compressed text databases with efficient query algorithms based on the compressed suffix arrays. In: Proc. 11th International Symposium on Algorithms and Computation. LNCS, vol. 1969, pp. 410–421. Springer, Heidelberg (2000)
Weiner, P.: Linear pattern matching algorithm. In: Proc. 14th Annual IEEE Symposium on Switching and Automata Theory, pp. 1–11 (1973)
Zhang, M.: Succinct Text Indexes on Large Alphabet. Technical Report, Jilin University (2005)
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Zhang, M., Tang, J., Guo, D., Hu, L., Li, Q. (2006). Succinct Text Indexes on Large Alphabet. In: Cai, JY., Cooper, S.B., Li, A. (eds) Theory and Applications of Models of Computation. TAMC 2006. Lecture Notes in Computer Science, vol 3959. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11750321_50
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DOI: https://doi.org/10.1007/11750321_50
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