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Succinct data structures for flexible text retrieval systems. (English) Zbl 1137.68360
Summary: We propose succinct data structures for text retrieval systems supporting document listing queries and ranking queries based on the tf*idf (term frequency times inverse document frequency) scores of documents. Traditional data structures for these problems support queries only for some predetermined keywords. Recently Muthukrishnan proposed a data structure for document listing queries for arbitrary patterns at the cost of data structure size. For computing the tf*idf scores there has been no efficient data structures for arbitrary patterns. Our new data structures support these queries using small space. The space is only $$2/\varepsilon$$ times the size of compressed documents plus $$10n$$ bits for a document collection of length $$n$$, for any 0$$<\varepsilon \leqslant$$1. This is much smaller than the previous $$O(n\log n)$$ bit data structures. Query time is $$O(m+q\log^\varepsilon n)$$ for listing and computing tf*idf scores for all $$q$$ documents containing a given pattern of length $$m$$. Our data structures are flexible in a sense that they support queries for arbitrary patterns.

##### MSC:
 68P05 Data structures 68P20 Information storage and retrieval of data 68T10 Pattern recognition, speech recognition
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##### References:
 [1] S. Muthukrishnan, Efficient algorithms for document retrieval problems, in: Proc. ACM-SIAM SODA, 2002, pp. 657-666 · Zbl 1093.68588 [2] Blumer, A.; Blumer, J.; Haussler, D.; McConnell, R.; Ehrenfeucht, A., Complete inverted files for efficient text retrieval and analysis, Journal of the ACM, 34, 3, 578-595, (1987) [3] 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) · Zbl 1092.68115 [4] R. Grossi, A. Gupta, J.S. Vitter, Higher order entropy analysis of compressed suffix arrays, in: DIMACS Workshop on Data Compression in Networks and Applications, 2003, pp. 841-850 · Zbl 1092.68584 [5] K. Sadakane, Succinct representations of lcp information and improvements in the compressed suffix arrays, in: Proc. ACM-SIAM SODA, 2002, pp. 225-232 · Zbl 1093.68578 [6] Sadakane, K., New text indexing functionalities of the compressed suffix arrays, Journal of algorithms, 48, 2, 294-313, (2003) · Zbl 1100.68563 [7] Ferragina, P.; Manzini, G., Indexing compressed texts, Journal of the ACM, 52, 4, 552-581, (2005) · Zbl 1323.68261 [8] Salton, G.; Wong, A.; Yang, C.S., A vector space model for automatic indexing, Communications of the ACM, 18, 11, 613-620, (1975) · Zbl 0313.68082 [9] Manber, U.; Myers, G., Suffix arrays: a new method for on-line string searches, SIAM journal on computing, 22, 5, 935-948, (1993) · Zbl 0784.68027 [10] P. Weiner, Linear pattern matching algorithms, in: Proceedings of the 14th IEEE Symposium on Switching and Automata Theory, 1973, pp. 1-11 [11] M. Farach, Optimal suffix tree construction with large alphabets, in: 38th IEEE Symp. on Foundations of Computer Science, 1997, pp. 137-143 [12] Gusfield, D., Algorithms on strings, trees, and sequences, (1997), Cambridge University Press · Zbl 0934.68103 [13] Munro, J.I.; Raman, V., Succinct representation of balanced parentheses and static trees, SIAM journal on computing, 31, 3, 762-776, (2001) · Zbl 1017.68037 [14] Munro, J.I.; Raman, V.; Rao, S.S., Space efficient suffix trees, Journal of algorithms, 39, 2, 205-222, (2001) · Zbl 0977.68069 [15] Ferragina, P.; Manzini, G.; Mäkinen, V.; Navarro, G., Succinct representation of sequences, (August 2004), Technical Report TR/DCC-2004-5, Dept. of Computer Science, Univ. of Chile [16] Bender, M.; Farach-Colton, M., The LCA problem revisited, (), 88-94 · Zbl 0959.68133 [17] R. Raman, V. Raman, S.S. Rao, Succinct indexable dictionaries with applications to encoding k-array trees and multisets, in: Proc. ACM-SIAM SODA, 2002, pp. 233-242 · Zbl 1093.68582 [18] A. Andersson, T. Hagerup, S. Nilsson, R. Raman, Sorting in linear time?, in: ACM Symposium on Theory of Computing, 1995, pp. 427-436 · Zbl 0968.68509 [19] Hui, L., Color set size problem with applications to string matching, (), 227-240
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