Abstract
Compact directed acyclic word graphs (CDAWGs) [Blumer et al. 1987] are a fundamental data structure on strings with applications in text pattern searching, data compression, and pattern discovery. Intuitively, the CDAWG of a string T is obtained by merging isomorphic subtrees of the suffix tree [Weiner 1973] of the same string T, thus CDAWGs are a compact indexing structure. In this paper, we investigate the sensitivity of CDAWGs when a single character edit operation (insertion, deletion, or substitution) is performed at the left-end of the input string T, namely, we are interested in the worst-case increase in the size of the CDAWG after a left-end edit operation. We prove that if \(\textsf{e}\) is the number of edges of the CDAWG for string T, then the number of new edges added to the CDAWG after a left-end edit operation on T is less than \(\textsf{e}\). Further, we present almost matching lower bounds on the sensitivity of CDAWGs for all cases of insertion, deletion, and substitution.
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References
Akagi, T., Funakoshi, M., Inenaga, S.: Sensitivity of string compressors and repetitiveness measures. Inf. Comput. 291, 104999 (2023). https://doi.org/10.1016/j.ic.2022.104999
Belazzougui, D., Cunial, F.: Fast label extraction in the CDAWG. In: SPIRE 2017, pp. 161–175 (2017). https://doi.org/10.1007/978-3-319-67428-5_14
Belazzougui, D., Cunial, F., Gagie, T., Prezza, N., Raffinot, M.: Composite repetition-aware data structures. In: CPM 2015, pp. 26–39 (2015). https://doi.org/10.1007/978-3-319-19929-0_3
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). https://doi.org/10.1145/28869.28873
Burrows, M., Wheeler, D.J.: A block sorting lossless data compression algorithm. Tech. Rep. 124, Digital Equipment Corporation (1994)
Crochemore, M., Vérin, R.: On compact directed acyclic word graphs. In: Mycielski, Jan, Rozenberg, Grzegorz, Salomaa, Arto (eds.) Structures in Logic and Computer Science. LNCS, vol. 1261, pp. 192–211. Springer, Heidelberg (1997). https://doi.org/10.1007/3-540-63246-8_12
Fujimaru, H., Nakashima, Y., Inenaga, S.: On sensitivity of compact directed acyclic word graphs. https://doi.org/10.48550/arXiv.2303.01726 CoRR abs/ arXiv: 2303.01726 (2023)
Inenaga, S., et al.: On-line construction of compact directed acyclic word graphs. Discret. Appl. Math. 146(2), 156–179 (2005). https://doi.org/10.1016/j.dam.2004.04.012
Kempa, D., Prezza, N.: At the roots of dictionary compression: string attractors. In: STOC 2018, pp. 827–840 (2018). https://doi.org/10.1145/3188745.3188814
Kociumaka, T., Navarro, G., Prezza, N.: Towards a definitive measure of repetitiveness. In: Kohayakawa, Y., Miyazawa, F.K. (eds.) LATIN 2021. LNCS, vol. 12118, pp. 207–219. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-61792-9_17
Radoszewski, J., Rytter, W.: On the structure of compacted subword graphs of Thue-Morse words and their applications. J. Dis. Algorithms 11, 15–24 (2012). https://doi.org/10.1016/j.jda.2011.01.001
Senft, M., Dvorák, T.: Sliding CDAWG perfection. In: SPIRE 2008, pp. 109–120 (2008). https://doi.org/10.1007/978-3-540-89097-3_12
Takagi, T., Goto, K., Fujishige, Y., Inenaga, S., Arimura, H.: Linear-size CDAWG: New repetition-aware indexing and grammar compression. In: SPIRE 2017, pp. 304–316 (2017). https://doi.org/10.1007/978-3-319-67428-5_26
Takeda, M., Matsumoto, T., Fukuda, T., Nanri, I.: Discovering characteristic expressions from literary works: a new text analysis method beyond n-gram statistics and KWIC. In: Discovery Science 2000, pp. 112–126 (2000). https://doi.org/10.1007/3-540-44418-1_10
Weiner, P.: Linear pattern matching algorithms. In: Proceedings of the 14th Annual Symposium on Switching and Automata Theory, pp. 1–11. IEEE (1973). https://doi.org/10.1109/SWAT.1973.13
Ziv, J., Lempel, A.: A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3), 337–343 (1977). https://doi.org/10.1109/TIT.1977.1055714
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Fujimaru, H., Nakashima, Y., Inenaga, S. (2023). On Sensitivity of Compact Directed Acyclic Word Graphs. In: Frid, A., Mercaş, R. (eds) Combinatorics on Words. WORDS 2023. Lecture Notes in Computer Science, vol 13899. Springer, Cham. https://doi.org/10.1007/978-3-031-33180-0_13
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