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Document retrieval with one wildcard. (English) Zbl 1339.68073
Summary: In this paper we extend several well-known document listing problems to the case when documents contain a substring that approximately matches the query pattern. We study the scenario when the query string can contain a wildcard symbol that matches any alphabet symbol; all documents that match a query pattern with one wildcard must be enumerated. We describe a linear space data structure that reports all documents containing a substring \(P\) in \(O(| P | + \sigma \sqrt{\log \log \log n} + {\mathtt docc})\) time, where \(\sigma\) is the alphabet size and is the number of listed documents. We also describe a succinct solution for this problem, as well as a solution for an extension of this problem. Furthermore our approach enables us to obtain an \(O(n \sigma)\)-space data structure that enumerates all documents containing both a pattern \(P_1\) and a pattern \(P_2\) in the special case when \(P_1\) and \(P_2\) differ in one symbol.
MSC:
68P20 Information storage and retrieval of data
68P05 Data structures
68W32 Algorithms on strings
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[1] Lewenstein, M.; Munro, J. I.; Nekrich, Y.; Thankachan, S. V., Document retrieval with one wildcard, (Mathematical Foundations of Computer Science MFCS, (2014)), 529-540 · Zbl 1339.68074
[2] Boyer, R. S.; Moore, J. S., A fast string searching algorithm, Commun. ACM, 20, 10, 762-772, (1977) · Zbl 1219.68165
[3] Knuth, D. E.; Morris, J. H.; Pratt, V. B., Fast pattern matching in strings, SIAM J. Comput., 6, 2, 323-350, (1977) · Zbl 0372.68005
[4] Hon, W.-K.; Shah, R.; Thankachan, S. V.; Vitter, J. S., Space-efficient frameworks for top-k string retrieval, J. ACM, 61, 2, 9, (2014) · Zbl 1295.68230
[5] Shah, R.; Sheng, C.; Thankachan, S. V.; Vitter, J. S., Top-k document retrieval in external memory, (Bodlaender, H. L.; Italiano, G. F., ESA, Lecture Notes in Comput. Sci., vol. 8125, (2013), Springer), 803-814 · Zbl 1394.68129
[6] Navarro, G.; Nekrich, Y., Top-k document retrieval in optimal time and linear space, (Rabani, Y., SODA, (2012), SIAM), 1066-1077
[7] Navarro, G., Spaces, trees, and colors: the algorithmic landscape of document retrieval on sequences, ACM Comput. Surv., 46, 4, 52, (2013) · Zbl 1305.68078
[8] Hon, W.-K.; Patil, M.; Shah, R.; Thankachan, S. V.; Vitter, J. S., Indexes for document retrieval with relevance, (Brodnik, A.; López-Ortiz, A.; Raman, V.; Viola, A., Space-Efficient Data Structures, Streams, and Algorithms, Lecture Notes in Comput. Sci., vol. 8066, (2013), Springer), 351-362 · Zbl 1394.68127
[9] Amir, A.; Keselman, D.; Landau, G. M.; Lewenstein, M.; Lewenstein, N.; Rodeh, M., Text indexing and dictionary matching with one error, J. Algorithms, 37, 2, 309-325, (2000) · Zbl 0966.68062
[10] Bille, P.; Gørtz, I. L.; Vildhøj, H. W.; Vind, S., String indexing for patterns with wildcards, (SWAT, (2012)), 283-294 · Zbl 1357.68306
[11] Cole, R.; Gottlieb, L.-A.; Lewenstein, M., Dictionary matching and indexing with errors and don’t cares, (Proc. 36th Annual ACM Symposium on Theory of Computing (STOC 2004), (2004)), 91-100 · Zbl 1192.68818
[12] Lewenstein, M., Indexing with gaps, (SPIRE, (2011)), 135-143
[13] Tam, A.; Wu, E.; Lam, T. W.; Yiu, S.-M., Succinct text indexing with wildcards, (SPIRE, (2009)), 39-50
[14] Lewenstein, M.; Nekrich, Y.; Vitter, J. S., Space-efficient string indexing for wildcard pattern matching, (Proc. 31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014), (2014)), 506-517 · Zbl 1359.68339
[15] Iliopoulos, C. S.; Rahman, M. S., Indexing factors with gaps, Algorithmica, 55, 1, 60-70, (2009) · Zbl 1180.68127
[16] Hon, W.-K.; Ku, T.-H.; Shah, R.; Thankachan, S. V.; Vitter, J. S., Compressed dictionary matching with one error, (Proc. 2011 Data Compression Conference (DCC 2011), (2011)), 113-122
[17] Lam, T. W.; Sung, W.-K.; Tam, S.-L.; Yiu, S.-M., Space efficient indexes for string matching with don’t cares, (ISAAC, (2007)), 846-857 · Zbl 1193.68293
[18] Rahman, M. S.; Iliopoulos, C. S., Pattern matching algorithms with don’t cares, (Proc. 33rd Conference on Current Trends in Theory and Practice of Computer Science (SOFSEM 2007), (2007)), 116-126
[19] Huynh, T. N.; Hon, W.-K.; Lam, T.-W.; Sung, W.-K., Approximate string matching using compressed suffix arrays, Theoret. Comput. Sci., 352, 1, 240-249, (2006) · Zbl 1086.68038
[20] Lewenstein, M., Orthogonal range searching for text indexing, (Space-Efficient Data Structures, Streams, and Algorithms - Papers in Honor of J. Ian Munro on the Occasion of His 66th Birthday, (2013)), 267-302 · Zbl 1394.68099
[21] Bille, P.; Gørtz, I. L., Substring range reporting, (Proc. 22nd Annual Symposium on Combinatorial Pattern Matching (CPM 2011), (2011)), 299-308 · Zbl 1339.68049
[22] Lewenstein, M.; Munro, J. I.; Raman, V.; Thankachan, S. V., Less space: indexing for queries with wildcards, (Algorithms and Computation - Proceedings of the 24th International Symposium, ISAAC 2013, Hong Kong, China, December 16-18, 2013, (2013)), 89-99 · Zbl 1329.68315
[23] Matias, Y.; Muthukrishnan, S.; Sahinalp, S. C.; Ziv, J., Augmenting suffix trees, with applications, (ESA ’98, (1998), Springer-Verlag London, UK), 67-78
[24] Muthukrishnan, S., Efficient algorithms for document retrieval problems, (Proc. 13th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2002), (2002)), 657-666 · Zbl 1093.68588
[25] Cohen, H.; Porat, E., Fast set intersection and two-patterns matching, Theoret. Comput. Sci., 411, 40-42, 3795-3800, (2010) · Zbl 1207.68270
[26] Hon, W.-K.; Shah, R.; Thankachan, S. V.; Vitter, J. S., String retrieval for multi-pattern queries, (String Processing and Information Retrieval - 17th International Symposium, (2010)), 55-66
[27] Fischer, J.; Gagie, T.; Kopelowitz, T.; Lewenstein, M.; Mäkinen, V.; Salmela, L.; Välimäki, N., Forbidden patterns, (LATIN, (2012)), 327-337 · Zbl 1353.68066
[28] Hon, W.-K.; Shah, R.; Thankachan, S. V.; Vitter, J. S., Document listing for queries with excluded pattern, (Proc. 23rd Annual Symposium on Combinatorial Pattern Matching (CPM 2012), (2012)), 185-195 · Zbl 1358.68093
[29] Fischer, J.; Heun, V., Space-efficient preprocessing schemes for range minimum queries on static arrays, SIAM J. Comput., 40, 2, 465-492, (2011) · Zbl 1222.05024
[30] Weiner, P., Linear pattern matching algorithms, (SWAT (FOCS), (1973), IEEE Computer Society), 1-11
[31] Manber, U.; Myers, E. W., Suffix arrays: a new method for on-line string searches, SIAM J. Comput., 22, 5, 935-948, (1993) · Zbl 0784.68027
[32] Belazzougui, D.; Navarro, G.; Valenzuela, D., Improved compressed indexes for full-text document retrieval, J. Discrete Algorithms, 18, 3-13, (2013) · Zbl 1268.68075
[33] Sadakane, K., Succinct data structures for flexible text retrieval systems, J. Discrete Algorithms, 5, 1, 12-22, (2007) · Zbl 1137.68360
[34] Sleator, D. D.; Tarjan, R. E., A data structure for dynamic trees, J. Comput. System Sci., 26, 3, 362-391, (1983) · Zbl 0509.68058
[35] Belazzougui, D.; Navarro, G., Alphabet-independent compressed text indexing, (Proc. 19th Annual European Symposium on Algorithms (ESA 2011), (2011)), 748-759 · Zbl 1325.68307
[36] Raman, R.; Raman, V.; Satti, S. R., Succinct indexable dictionaries with applications to encoding k-ary trees, prefix sums and multisets, ACM Trans. Algorithms, 3, 4, (2007)
[37] Munro, J. I.; Navarro, G.; Shah, R.; Thankachan, S. V., Ranked document selection, (SWAT, (2014)), 344-356 · Zbl 1416.68064
[38] Chan, T. M.; Larsen, K. G.; Patrascu, M., Orthogonal range searching on the ram, revisited, (Symposium on Computational Geometry, (2011)), 1-10 · Zbl 1283.68139
[39] Alstrup, S.; Brodal, G. S.; Rauhe, T., Optimal static range reporting in one dimension, (Proc. 33rd Annual ACM Symposium on Theory of Computing (STOC), (2001)), 476-482 · Zbl 1323.68536
[40] Lewenstein, M.; Nekrich, Y.; Vitter, J. S., Space-efficient string indexing for wildcard pattern matching, CoRR · Zbl 1359.68339
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