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Orthogonal Range Searching for Text Indexing

  • Chapter
Space-Efficient Data Structures, Streams, and Algorithms

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8066))

Abstract

Text indexing, the problem in which one desires to preprocess a (usually large) text for future (shorter) queries, has been researched ever since the suffix tree was invented in the early 70’s. With textual data continuing to increase and with changes in the way it is accessed, new data structures and new algorithmic methods are continuously required. Therefore, text indexing is of utmost importance and is a very active research domain.

Orthogonal range searching, classically associated with the computational geometry community, is one of the tools that has increasingly become important for various text indexing applications. Initially, in the mid 90’s there were a couple of results recognizing this connection. In the last few years we have seen an increase in use of this method and are reaching a deeper understanding of the range searching uses for text indexing.

In this monograph we survey some of these results.

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References

  1. Agarwal, P.K.: Range searching. In: Handbook of Discrete and Computational Geometry, pp. 575–598. CRC Press, Inc. (1997)

    Google Scholar 

  2. Alstrup, S., Brodal, G.S., Rauhe, T.: New data structures for orthogonal range searching. In: Proc. of Foundations of Computer Science (FOCS), pp. 198–207 (2000)

    Google Scholar 

  3. Amir, A., Apostolico, A., Landau, G.M., Levy, A., Lewenstein, M., Porat, E.: Range LCP. In: Asano, T., Nakano, S.-i., Okamoto, Y., Watanabe, O. (eds.) ISAAC 2011. LNCS, vol. 7074, pp. 683–692. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  4. Amir, A., Apostolico, A., Landau, G.M., Satta, G.: Efficient text fingerprinting via Parikh mapping. Journal of Discrete Algorithms 1(5-6), 409–421 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  5. Amir, A., Aumann, Y., Lewenstein, M., Porat, E.: Function matching. SIAM Journal on Computing 35(5), 1007–1022 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  6. Amir, A., Benson, G., Farach, M.: Let sleeping files lie: Pattern matching in z-compressed files. Journal of Computer and System Sciences 52(2), 299–307 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  7. Amir, A., Chencinski, E., Iliopoulos, C.S., Kopelowitz, T., Zhang, H.: Property matching and weighted matching. Theoretical Computer Science 395(2-3), 298–310 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  8. Amir, A., Fischer, J., Lewenstein, M.: Two-dimensional range minimum queries. In: Ma, B., Zhang, K. (eds.) CPM 2007. LNCS, vol. 4580, pp. 286–294. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  9. Amir, A., Francheschini, G., Grossi, R., Kopelowitz, T., Lewenstein, M., Lewenstein, N.: Managing unbounded-length keys in comparison-driven data structures with applications to on-line indexing. SIAM Journal on Computing (to appear, 2013)

    Google Scholar 

  10. Amir, A., Keselman, D., Landau, G.M., Lewenstein, M., Lewenstein, N., Rodeh, M.: Text indexing and dictionary matching with one error. Journal of Algorithms 37(2), 309–325 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  11. Amir, A., Landau, G.M., Lewenstein, M., Sokol, D.: Dynamic text and static pattern matching. ACM Transactions on Algorithms 3(2) (2007)

    Google Scholar 

  12. Arroyuelo, D., Navarro, G., Sadakane, K.: Stronger Lempel-Ziv based compressed text indexing. Algorithmica 62(1-2), 54–101 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  13. Atallah, M.J., Yuan, H.: Data structures for range minimum queries in multidimensional arrays. In: Proc. of the Symposium on Discrete Algorithms (SODA), pp. 150–160 (2010)

    Google Scholar 

  14. Badkobeh, G., Fici, G., Kroon, S., Lipták, Z.: Binary jumbled string matching for highly run-length compressible texts. Information Processing Letters 113, 604–608 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  15. Baker, B.S.: Parameterized pattern matching: Algorithms and applications. Journal of Computer and System Sciences 52(1), 28–42 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  16. Barbay, J., Claude, F., Navarro, G.: Compact binary relation representations with rich functionality. The Computing Research Repository (arXiv), abs/1201.3602 (2012)

    Google Scholar 

  17. Bialynicka-Birula, I., Grossi, R.: Rank-sensitive data structures. In: Consens, M.P., Navarro, G. (eds.) SPIRE 2005. LNCS, vol. 3772, pp. 79–90. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  18. Bille, P., Fischer, J., Gørtz, I.L., Kopelowitz, T., Sach, B., Vildhøj, H.W.: Sparse suffix tree construction in small space. In: Proc. of International Colloquium on Automata, Languages and Complexity, ICALP (2013)

    Google Scholar 

  19. Bille, P., Gørtz, I.L.: Substring range reporting. In: Giancarlo, R., Manzini, G. (eds.) CPM 2011. LNCS, vol. 6661, pp. 299–308. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  20. Bose, P., He, M., Maheshwari, A., Morin, P.: Succinct orthogonal range search structures on a grid with applications to text indexing. In: Dehne, F., Gavrilova, M., Sack, J.-R., Tóth, C.D. (eds.) WADS 2009. LNCS, vol. 5664, pp. 98–109. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  21. Brodal, G.S., Gąsieniec, L.: Approximate dictionary queries. In: Hirschberg, D.S., Meyers, G. (eds.) CPM 1996. LNCS, vol. 1075, pp. 65–74. Springer, Heidelberg (1996)

    Chapter  Google Scholar 

  22. Brodal, G.S., Davoodi, P., Lewenstein, M., Raman, R., Rao, S.S.: Two dimensional range minimum queries and Fibonacci lattices. In: Epstein, L., Ferragina, P. (eds.) ESA 2012. LNCS, vol. 7501, pp. 217–228. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  23. Brodal, G.S., Davoodi, P., Rao, S.S.: On space efficient two dimensional range minimum data structures. Algorithmica 63(4), 815–830 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  24. Brodnik, A., Munro, J.I.: Membership in constant time and almost-minimum space. SIAM Journal on Computing 28(5), 1627–1640 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  25. Butman, A., Eres, R., Landau, G.M.: Scaled and permuted string matching. Information Processing Letters 92(6), 293–297 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  26. Chan, H.-L., Lam, T.W., Sung, W.-K., Tam, S.-L., Wong, S.-S.: A linear size index for approximate pattern matching. Journal of Discrete Algorithms 9(4), 358–364 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  27. Chan, T.M.: Persistent predecessor search and orthogonal point location on the word ram. In: Proc. of Symposium on Discrete Algorithms (SODA), pp. 1131–1145 (2011)

    Google Scholar 

  28. Chan, T.M., Larsen, K.G., Pǎtraşcu, M.: Orthogonal range searching on the RAM, revisited. In: Proc. of the Symposium on Computational Geometry, SOCG (2011)

    Google Scholar 

  29. Chazelle, B.: A functional approach to data structures and its use in multidimensional searching. SIAM Journal on Computing 17(3), 427–462 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  30. Chazelle, B.: Lower bounds for orthogonal range searching: I. the reporting case. Journal of the ACM 37(2), 200–212 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  31. Chazelle, B., Rosenberg, B.: The complexity of computing partial sums off-line. International Journal of Computational Geometry and Applications 1(1), 33–45 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  32. Chien, Y.-F., Hon, W.-K., Shah, R., Thankachan, S.V., Vitter, J.S.: Geometric Burrows-Wheeler transform: Compressed text indexing via sparse suffixes and range searching. Algorithmica (to appear, 2013)

    Google Scholar 

  33. Cicalese, F., Fici, G., Lipták, Z.: Searching for jumbled patterns in strings. In: Holub, J., Zdárek, J. (eds.) Proceedings of the Prague Stringology Conference (PSC), pp. 105–117 (2009)

    Google Scholar 

  34. Claude, F., Navarro, G.: Self-indexed grammar-based compression. Fundamenta Informaticae 111(3), 313–337 (2011)

    MathSciNet  MATH  Google Scholar 

  35. Claude, F., Navarro, G.: Improved grammar-based compressed indexes. In: Calderón-Benavides, L., González-Caro, C., Chávez, E., Ziviani, N. (eds.) SPIRE 2012. LNCS, vol. 7608, pp. 180–192. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  36. Cole, R., Gottlieb, L.-A., Lewenstein, M.: Dictionary matching and indexing with errors and don’t cares. In: Proc. of Symposium on Theory of Computing (STOC), pp. 91–100 (2004)

    Google Scholar 

  37. Cormode, G., Muthukrishnan, S.: Substring compression problems. In: Proc. of Symposium on Discrete Algorithms (SODA), pp. 321–330 (2005)

    Google Scholar 

  38. Crochemore, M., Iliopoulos, C.S., Kubica, M., Rahman, M.S., Tischler, G., Walen, T.: Improved algorithms for the range next value problem and applications. Theoretical Computer Science 434, 23–34 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  39. Crochemore, M., Iliopoulos, C.S., Rahman, M.S.: Finding patterns in given intervals. In: Kučera, L., Kučera, A. (eds.) MFCS 2007. LNCS, vol. 4708, pp. 645–656. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  40. Crochemore, M., Kubica, M., Walen, T., Iliopoulos, C.S., Rahman, M.S.: Finding patterns in given intervals. Fundamenta Informaticae 101(3), 173–186 (2010)

    MathSciNet  MATH  Google Scholar 

  41. Davoodi, P., Landau, G., Lewenstein, M.: Multi-dimensional range minimum queries (manuscript, 2013)

    Google Scholar 

  42. Davoodi, P., Raman, R., Satti, S.R.: Succinct representations of binary trees for range minimum queries. In: Gudmundsson, J., Mestre, J., Viglas, T. (eds.) COCOON 2012. LNCS, vol. 7434, pp. 396–407. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  43. Demaine, E.D., Landau, G.M., Weimann, O.: On cartesian trees and range minimum queries. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds.) ICALP 2009, Part I. LNCS, vol. 5555, pp. 341–353. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  44. Demaine, E.D., López-Ortiz, A.: A linear lower bound on index size for text retrieval. Journal of Algorithms 48(1), 2–15 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  45. Dietz, P.F., Raman, R.: Persistence, amortization and randomization. In: Proc. of Symposium on Discrete Algorithms (SODA), pp. 78–88 (1991)

    Google Scholar 

  46. Farach, M., Muthukrishnan, S.: Perfect hashing for strings: Formalization and algorithms. In: Hirschberg, D.S., Meyers, G. (eds.) CPM 1996. LNCS, vol. 1075, pp. 130–140. Springer, Heidelberg (1996)

    Chapter  Google Scholar 

  47. Farach, M., Thorup, M.: String matching in Lempel-Ziv compressed strings. Algorithmica 20(4), 388–404 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  48. Farach-Colton, M., Ferragina, P., Muthukrishnan, S.: On the sorting-complexity of suffix tree construction. Journal of the ACM 47(6), 987–1011 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  49. Ferragina, P.: Dynamic text indexing under string updates. Journal of Algorithms 22(2), 296–328 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  50. Ferragina, P., Manzini, G.: Indexing compressed text. Journal of the ACM 52(4), 552–581 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  51. Ferragina, P., Muthukrishnan, S., de Berg, M.: Multi-method dispatching: A geometric approach with applications to string matching problems. In: Proc. of Symposium on Theory of Computing (STOC), pp. 483–491 (1999)

    Google Scholar 

  52. Fischer, J., Gagie, T., Kopelowitz, T., Lewenstein, M., Mäkinen, V., Salmela, L., Välimäki, N.: Forbidden patterns. In: Fernández-Baca, D. (ed.) LATIN 2012. LNCS, vol. 7256, pp. 327–337. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  53. Fischer, J., Heun, V.: Space-efficient preprocessing schemes for range minimum queries on static arrays. SIAM Journal on Computing 40(2), 465–492 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  54. Gabow, H.N., Bentley, J.L., Tarjan, R.E.: Scaling and related techniques for geometry problems. In: Proc. of the Symposium on Theory of Computing (STOC), pp. 135–143 (1984)

    Google Scholar 

  55. Gagie, T., Gawrychowski, P., Kärkkäinen, J., Nekrich, Y., Puglisi, S.J.: A faster grammar-based self-index. In: Dediu, A.-H., Martín-Vide, C. (eds.) LATA 2012. LNCS, vol. 7183, pp. 240–251. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  56. Golin, M., Iacono, J., Krizanc, D., Raman, R., Rao, S.S.: Encoding 2D range maximum queries. In: Asano, T., Nakano, S.-I., Okamoto, Y., Watanabe, O. (eds.) ISAAC 2011. LNCS, vol. 7074, pp. 180–189. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  57. Golynski, A., Munro, J.I., Rao, S.S.: Rank/select operations on large alphabets: a tool for text indexing. In: Proc. of Symposium on Discrete Algorithms (SODA), pp. 368–373 (2006)

    Google Scholar 

  58. Grossi, R., Gupta, A., Vitter, J.S.: High-order entropy-compressed text indexes. In: Proc. of Symposium on Discrete Algorithms (SODA), pp. 841–850 (2003)

    Google Scholar 

  59. 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)

    Article  MathSciNet  MATH  Google Scholar 

  60. Gusfield, D.: Algorithms on strings, trees, and sequences: computer science and computational biology. Cambridge University Press (1997)

    Google Scholar 

  61. Harel, D., Tarjan, R.E.: Fast algorithms for finding nearest common ancestors. SIAM Journal on Computing 13(2), 338–355 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  62. Hon, W.-K., Ku, T.-H., Shah, R., Thankachan, S.V., Vitter, J.S.: Compressed dictionary matching with one error. In: Proc. of the Data Compression Conference (DCC), pp. 113–122 (2011)

    Google Scholar 

  63. Hon, W.-K., Patil, M., Shah, R., Thankachan, S.V.: Compressed property suffix trees. In: Proc. of the Data Compression Conference (DCC), pp. 123–132 (2011)

    Google Scholar 

  64. Hon, W.-K., Shah, R., Thankachan, S.V., Vitter, J.S.: On position restricted substring searching in succinct space. Journal of Discrete Algorithms 17, 109–114 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  65. Hon, W.-K., Shah, R., Vitter, J.S.: Space-efficient framework for top-k string retrieval problems. In: Proc. of Foundations of Computer Science (FOCS), pp. 713–722 (2009)

    Google Scholar 

  66. Iliopoulos, C.S., Rahman, M.S.: Faster index for property matching. Information Processing Letters 105(6), 218–223 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  67. Iliopoulos, C.S., Rahman, M.S.: Indexing factors with gaps. Algorithmica 55(1), 60–70 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  68. Jacobson, G.: Space-efficient static trees and graphs. In: FOCS, pp. 549–554 (1989)

    Google Scholar 

  69. Juan, M.T., Liu, J.J., Wang, Y.L.: Errata for “faster index for property matching“. Information Processing Letters 109(18), 1027–1029 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  70. Kärkkäinen, J.: Repetition-Based Text Indexes. PhD thesis, University of Helsinki, Finland (1999)

    Google Scholar 

  71. Kärkkäinen, J., Sanders, P., Burkhardt, S.: Linear work suffix array construction. Journal of the ACM 53(6), 918–936 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  72. Kärkkäinen, J., Ukkonen, E.: Lempel-Ziv parsing and sublinear-size index structures for string matching. In: Proc. 3rd South American Workshop on String Processing (WSP). International Informatics Series 4, pp. 141–155. Carleton University Press (1996)

    Google Scholar 

  73. Kärkkäinen, J., Ukkonen, E.: Sparse suffix trees. In: Cai, J.-Y., Wong, C.K. (eds.) COCOON 1996. LNCS, vol. 1090, pp. 219–230. Springer, Heidelberg (1996)

    Chapter  Google Scholar 

  74. Karpinski, M., Nekrich, Y.: Top-k color queries for document retrieval. In: Proc. of Symposium on Discrete Algorithms (SODA), pp. 401–411 (2011)

    Google Scholar 

  75. Keller, O., Kopelowitz, T., Landau, S., Lewenstein, M.: Generalized substring compression. In: Kucherov, G., Ukkonen, E. (eds.) CPM 2009 Lille. LNCS, vol. 5577, pp. 26–38. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  76. Keller, O., Kopelowitz, T., Lewenstein, M.: Range non-overlapping indexing and successive list indexing. In: Dehne, F., Sack, J.-R., Zeh, N. (eds.) WADS 2007. LNCS, vol. 4619, pp. 625–636. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  77. Kopelowitz, T.: The property suffix tree with dynamic properties. In: Amir, A., Parida, L. (eds.) CPM 2010. LNCS, vol. 6129, pp. 63–75. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  78. Kopelowitz, T., Kucherov, G., Nekrich, Y., Starikovskaya, T.A.: Cross-document pattern matching. Journal of Discrete Algorithms (to appear, 2013)

    Google Scholar 

  79. Kopelowitz, T., Lewenstein, M.: Dynamic weighted ancestors. In: Proc. of Symposium on Discrete Algorithms (SODA), pp. 565–574 (2007)

    Google Scholar 

  80. Kopelowitz, T., Lewenstein, M., Porat, E.: Persistency in suffix trees with applications to string interval problems. In: Grossi, R., Sebastiani, F., Silvestri, F. (eds.) SPIRE 2011. LNCS, vol. 7024, pp. 67–80. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  81. Kreft, S., Navarro, G.: On compressing and indexing repetitive sequences. Theoretical Computer Science 483, 115–133 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  82. Landau, G.M., Vishkin, U.: Fast string matching with k differences. Journal of Computer and System Sciences 37(1), 63–78 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  83. Lenhof, H.-P., Smid, M.H.M.: Using persistent data structures for adding range restrictions to searching problems. Theoretical Informatics and Applications (ITA) 28(1), 25–49 (1994)

    MathSciNet  MATH  Google Scholar 

  84. Levenshtein, V.I.: Binary codes capable of correcting deletions, insertions, and reversals. Soviet Physics Doklady 10, 707–710 (1966)

    MathSciNet  MATH  Google Scholar 

  85. Lewenstein, M.: Parameterized matching. In: Encyclopedia of Algorithms (2008)

    Google Scholar 

  86. Mäkinen, V., Navarro, G.: Position-restricted substring searching. In: Correa, J.R., Hevia, A., Kiwi, M. (eds.) LATIN 2006. LNCS, vol. 3887, pp. 703–714. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  87. Manber, U., Myers, E.W.: Suffix arrays: A new method for on-line string searches. SIAM Journal on Computing 22(5), 935–948 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  88. McCreight, E.M.: A space-economical suffix tree construction algorithm. Journal of the ACM 23(2), 262–272 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  89. Moosa, T.M., Rahman, M.S.: Indexing permutations for binary strings. Information Processing Letters 110(18-19), 795–798 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  90. Muthukrishnan, S.: Efficient algorithms for document retrieval problems. In: Proc. of the Symposium on Discrete Algorithms (SODA), pp. 657–666 (2002)

    Google Scholar 

  91. Navarro, G.: Wavelet trees for all. In: Kärkkäinen, J., Stoye, J. (eds.) CPM 2012. LNCS, vol. 7354, pp. 2–26. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  92. Navarro, G.: Spaces, trees and colors: The algorithmic landscape of document retrieval on sequences. The Computing Research Repository (arXiv), abs/1304.6023 (2013)

    Google Scholar 

  93. Navarro, G., Mäkinen, V.: Compressed full-text indexes. ACM Computing Surveys 39(1), 2 (2007)

    Article  MATH  Google Scholar 

  94. Navarro, G., Nekrich, Y.: Top-k document retrieval in optimal time and linear space. In: Proc. of Symposium on Discrete Algorithms (SODA), pp. 1066–1077 (2012)

    Google Scholar 

  95. Nekrich, Y., Navarro, G.: Sorted range reporting. In: Fomin, F.V., Kaski, P. (eds.) SWAT 2012. LNCS, vol. 7357, pp. 271–282. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  96. Russo, L.M.S., Oliveira, A.L.: A compressed self-index using a Ziv-Lempel dictionary. Information Retrieval 11(4), 359–388 (2008)

    Article  Google Scholar 

  97. Sadakane, K.: Succinct data structures for flexible text retrieval systems. Journal of Discrete Algorithms 5(1), 12–22 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  98. Shah, R., Sheng, C., Thankachan, S.V., Vitter, J.S.: On optimal top-k string retrieval. The Computing Research Repository (arXiv), abs/1207.2632 (2012)

    Google Scholar 

  99. Thankachan, S.V.: Compressed indexes for aligned pattern matching. In: Grossi, R., Sebastiani, F., Silvestri, F. (eds.) SPIRE 2011. LNCS, vol. 7024, pp. 410–419. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  100. Tsur, D.: Fast index for approximate string matching. Journal of Discrete Algorithms 8(4), 339–345 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  101. Ukkonen, E.: On-line construction of suffix trees. Algorithmica 14(3), 249–260 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  102. van Emde Boas, P.: Preserving order in a forest in less than logarithmic time and linear space. Information Processing Letters 6(3), 80–82 (1977)

    Article  MATH  Google Scholar 

  103. Vuillemin, J.: A unifying look at data structures. Communications of the ACM 23(4), 229–239 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  104. Weiner, P.: Linear pattern matching algorithm. In: Proc. of the Symposium on Switching and Automata Theory, pp. 1–11 (1973)

    Google Scholar 

  105. Willard, D.E.: Log-logarithmic worst-case range queries are possible in space θ(n). Information Processing Letters 17(2), 81–84 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  106. Yu, C.-C., Hon, W.-K., Wang, B.-F.: Improved data structures for the orthogonal range successor problem. Computational Geometry 44(3), 148–159 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  107. Ziv, J., Lempel, A.: A universal algorithm for sequential data compression. IEEE Transactions on Information Theory 23(3), 337–343 (1977)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Bar-Ilan University, Israel

    Moshe Lewenstein

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  1. Moshe Lewenstein
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  1. Faculty of Computer and Information Science, University of Ljubljana, Ljubljana, Slovenia

    Andrej Brodnik

  2. Cheriton School of Computer Science, University of Waterloo, Waterloo, ON, Canada

    Alejandro López-Ortiz

  3. The Institute of Mathematical Sciences, Chennai, India

    Venkatesh Raman

  4. Facultad de Ingeniería, Universidad de la República, Montevideo, Uruguay

    Alfredo Viola

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Lewenstein, M. (2013). Orthogonal Range Searching for Text Indexing. In: Brodnik, A., López-Ortiz, A., Raman, V., Viola, A. (eds) Space-Efficient Data Structures, Streams, and Algorithms. Lecture Notes in Computer Science, vol 8066. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40273-9_18

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