Abstract
Given an n-length text over a σ-size alphabet, we propose a dynamic rank-select structure that supports \(O((1+\frac{\log\sigma}{\log\log n})\log n)\) time operations in nlogσ + o(nlogσ) bits space. If σ < logn, then the operation time is O(logn). In addition, we consider both static and dynamic rank-select structures on the run-length encoding (RLE) of a text. For an n′-length RLE of an n-length text, we present a static structure that gives O(1) time select and O(loglogσ) time rank using n′logσ + O(n) bits and a dynamic structure that provides \(O((1+\frac{\log\sigma}{\log\log n})\log n)\) time operations in n′logσ + o(n′logσ) + O(n) bits.
This work was supported by FPR05A2-341 of 21C Frontier Functional Proteomics Project from Korean Ministry of Science & Technology.
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References
Chan, H.-L., Hon, W.-K., Lam, T.-W.: Compressed index for a dynamic collection of texts. In: Proceedings of the 15th Annual Symposium on Combinatorial Pattern Matching, pp. 445–456 (2004)
Clark, D.R.: Compact Pat Trees. PhD thesis, Univ. Waterloo (1998)
Ferragina, P., Luccio, F., Manzini, G., Muthukrishnan, S.: Structuring labeled trees for optimal succinctness, and beyond. In: Proceedings of the IEEE Symposium on Foundations of Computer Science, pp. 184–196 (2005)
Ferragina, P., Manzini, G.: Indexing compressed text. Journal of ACM 52(4), 552–581 (2005)
Ferragina, P., Manzini, G., Mäkinen, V., Navarro, G.: Succinct representation of sequences and full-text indexes. ACM Transactions on Algorithms (to appear)
Golynski, A., Munro, J.I., Rao, S.S.: Rank/select operations on large alphabets: a tool for text indexing. In: Proceedings of the 17th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 368–373 (2006)
Grossi, R., Gupta, A., Vitter, J.S.: High-order entropy-compresssed text indexes. In: Proceedings of the 14th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 841–850 (2003)
Grossi, R., Vitter, J.S.: Compressed suffix arrays and suffix trees with applications to text indexing and string matching. SIAM Journal on Computing 35(2), 378–407 (2005)
Gupta, A., Hon, W.-K., Shah, R., Vitter, J.S.: Dynamic rank/select dictionaries with applications to xml indexing. Manuscript (2006)
Hon, W.-K., Sadakane, K., Sung, W.-K.: Breaking a time–and–space barrier in constructing full–text indices. In: Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science, pp. 251–260 (2003)
Hon, W.-K., Sadakane, K., Sung, W.-K.: Succinct data structures for searchable partial sums. In: Proceedings of the 14th Annual Symposium on Algorithms and Computation, pp. 505–516 (2003)
Jacobson, G.: Space-efficient static trees and graphs. In: Proceedings of the 30th Annual IEEE Symposium on Foundations of Computer Science, pp. 549–554 (1989)
Kim, D.-K., Na, J.-C., Kim, J.-E., Park, K.: Fast computation of rank and select functions for succinct representation. Manuscript (2006)
Mäkinen, V., Navarro, G.: Succinct suffix arrays based on run-length encoding. In: Proceedings of the 16th Annual Symposium on Combinatorial Pattern Matching, pp. 45–56 (2005)
Mäkinen, V., Navarro, G.: Dynamic entropy-compressed sequences and full-text indexes. In: Proceedings of the 17th Annual Symposium on Compinatorial Pattern Matching, pp. 306–317 (2006)
Manzini, G.: An analysis of the burrows-wheeler transform. Journal of ACM 48(3), 407–430 (2001)
Miltersen, P.B.: Lower bounds on the size of selection and rank indexes. In: Proceedings of the 16th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 11–12 (2005)
Munro, J.I.: Tables. In: Proceedings of the 16th Conference on Foundations of Software Technology and Theoretical Computer Science, pp. 37–42 (1996)
Munro, J.I., Raman, R., Raman, V., Rao, S.S.: Succinct representations of permutations. In: Proceedings of the 30th International Colloquium on Automata, Language, and Programming, pp. 345–356 (2003)
Munro, J.I., Raman, V.: Succinct representations of balanced parentheses and static trees. SIAM Journal on Computing 31(3), 762–776 (2001)
Munro, J.I., Rao, S.S.: Succinct representations of functions. In: Proceedings of the 31st International Colloquium on Automata, Languages, and Programming, pp. 1006–1015 (2004)
Raman, R., Raman, V., Rao, S.S.: Succinct dynamic data structures. In: Proceedings of the 7th International Workshop on Algorithms and Data Structures, pp. 426–437 (2001)
Raman, R., Raman, V., Rao, S.S.: Succinct indexable dictionaries with applications to encoding k-ary trees and multisets. In: Proceedings of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 233–242 (2002)
Sadakane, K.: New text indexing functionalites of the compressed suffix arrays. Journal of Algorithms 48(2), 294–313 (2003)
Sadakane, K., Grossi, R.: Squeezing succinct data structures into entropy bounds. In: Proceedings of the 17-th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1230–1239 (2006)
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Lee, S., Park, K. (2007). Dynamic Rank-Select Structures with Applications to Run-Length Encoded Texts. In: Ma, B., Zhang, K. (eds) Combinatorial Pattern Matching. CPM 2007. Lecture Notes in Computer Science, vol 4580. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73437-6_12
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DOI: https://doi.org/10.1007/978-3-540-73437-6_12
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