Abstract
This paper considers enumeration of substring equivalence classes introduced by Blumer et al. [1]. They used the equivalence classes to define an index structure called compact directed acyclic word graphs (CDAWGs). In text analysis, considering these equivalence classes is useful since they group together redundant substrings with essentially identical occurrences. In this paper, we present how to enumerate those equivalence classes using suffix arrays. Our algorithm uses rank and lcp arrays for traversing the corresponding suffix trees, but does not need any other additional data structure. The algorithm runs in linear time in the length of the input string. We show experimental results comparing the running times and space consumptions of our algorithm, suffix tree and CDAWG based approaches.
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Blumer, A., Blumer, J., Haussler, D., Mcconnell, R., Ehrenfeucht, A.: Complete inverted files for efficient text retrieval and analysis. J. ACM 34(3), 578–595 (1987)
Narisawa, K., Bannai, H., Hatano, K., Takeda, M.: Unsupervised spam detection based on string alienness measures. Technical report, Department of Informatics, Kyushu University (2007)
Takeda, M., Matsumoto, T., Fukuda, T., Nanri, I.: Discovering characteristic expressions in literary works. Theoretical Computer Science 292(2), 525–546 (2003)
Inenaga, S., Hoshinoa, H., Shinohara, A., Takeda, M., Arikawa, S., Mauri, G., Pavesi, G.: On-line construction of compact directed acyclic word graphs. Discrete Applied Mathematics 146(2), 156–179 (2005)
Weiner, P.: Linear pattern matching algorithms. In: Proc. 14th IEEE Annual Symp. on Switching and Automata Theory, pp. 1–11 (1973)
Ukkonen, E.: On-line construction of suffix trees. Algorithmica 14(3), 249–260 (1995)
Manber, U., Myers, G.: Suffix arrays: a new method for on-line string searches. SIAM J. Computing 22(5), 935–948 (1993)
Kasai, T., Lee, G., Arimura, H., Arikawa, S., Park, K.: Linear-time Longest-Common-Prefix Computation in Suffix Arrays and Its Applications. In: Amir, A., Landau, G.M. (eds.) CPM 2001. LNCS, vol. 2089, pp. 181–192. Springer, Heidelberg (2001)
Abouelhoda, M.I., Kurtz, S., Ohlebusch, E.: Replacing suffix trees with enhanced suffix arrays. Journal of Discrete Algorithms 2(1), 53–86 (2004)
Blumer, A., Blumer, J., Haussler, D., Ehrenfeucht, A., Chen, M.T., Seiferas, J.: The smallest automaton recognizing the subwords of a text. Theoretical Computer Science 40, 31–55 (1985)
McCreight, E.M.: A space-economical suffix tree construction algorithm. J. ACM 23(2), 262–272 (1976)
Kärkkäinen, J., Sanders, P.: Simple linear work suffix array construction. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 943–955. Springer, Heidelberg (2003)
Kim, D.K., Sim, J.S., Park, H., Park, K.: Linear-time construction of suffix arrays. In: Baeza-Yates, R.A., Chávez, E., Crochemore, M. (eds.) CPM 2003. LNCS, vol. 2676, pp. 186–199. Springer, Heidelberg (2003)
Ko, P., Aluru, S.: Space efficient linear time construction of suffix arrays. In: Baeza-Yates, R.A., Chávez, E., Crochemore, M. (eds.) CPM 2003. LNCS, vol. 2676, pp. 200–210. Springer, Heidelberg (2003)
Arnold, R., Bell, T.: A corpus for the evaluation of lossless compression algorithms. In: Proc. DCC ’97, pp. 201–210 (1997), http://corpus.canterbury.ac.nz/
Nevill-Manning, C., Witten, I.: Protein is incompressible. In: Proc. DCC 1999, pp. 257–266 (1999), http://www.data-compression.info/Corpora/ProteinCorpus/index.htm
Larsson, N.J., Sadakane, K.: Faster suffix sorting. Technical Report LU-CS-TR:99-214, LUNDFD6/(NFCS-3140)/1–20/(1999) Department of Computer Science, Lund University, Sweden (1999), http://www.larsson.dogma.net/qsufsort.c
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Narisawa, K., Inenaga, S., Bannai, H., Takeda, M. (2007). Efficient Computation of Substring Equivalence Classes with Suffix Arrays. 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_34
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DOI: https://doi.org/10.1007/978-3-540-73437-6_34
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