Abstract
Kreft and Navarro [DCC 2010] introduced a restricted variant of the well-known Lempel-Ziv factorization, called the LZ-End factorization. Only recently Kempa and Saha [SODA2022] were able to obtain a good upper bound on the size of the LZ-End factorization in terms of the size of the LZ factorization. We extend their approach to improve the upper bound by a doubly-logarithmic factor.
Maria Kosche’s work was supported by the DFG project number 389613931. Florin Manea’s work was supported by the DFG Heisenberg-project number 466789228.
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References
Alakuijala, J., et al.: Brotli: a general-purpose data compressor. ACM Trans. Inf. Syst. (TOIS) 37(1), 1–30 (2018)
Bannai, H., Funakoshi, M., Kurita, K., Nakashima, Y., Seto, K., Uno, T.: Optimal LZ-End parsing is hard. In: CPM. LIPIcs, vol. 259, pp. 3:1–3:11. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)
Collet, Y., Kucherawy, M.: Zstandard compression and the application/zstd media type. Techical report (2018)
Goto, K., Bannai, H.: Simpler and faster Lempel Ziv factorization. In: DCC, pp. 133–142. IEEE (2013)
Ideue, T., Mieno, T., Funakoshi, M., Nakashima, Y., Inenaga, S., Takeda, M.: On the approximation ratio of LZ-End to LZ77. In: Lecroq, T., Touzet, H. (eds.) SPIRE 2021. LNCS, vol. 12944, pp. 114–126. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-86692-1_10
Kärkkäinen, J., Kempa, D., Puglisi, S.J.: Linear time Lempel-Ziv factorization: simple, fast, small. In: Fischer, J., Sanders, P. (eds.) CPM 2013. LNCS, vol. 7922, pp. 189–200. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-38905-4_19
Kempa, D., Kosolobov, D.: LZ-end parsing in compressed space. In: DCC, pp. 350–359. IEEE (2017)
Kempa, D., Kosolobov, D.: LZ-end parsing in linear time. In: ESA. LIPIcs, vol. 87, pp. 53:1–53:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)
Kempa, D., Puglisi, S.J.: Lempel-Ziv factorization: simple, fast, practical. In: ALENEX, pp. 103–112. SIAM (2013)
Kempa, D., Saha, B.: An upper bound and linear-space queries on the LZ-End parsing. In: SODA, pp. 2847–2866. SIAM (2022)
Kreft, S., Navarro, G.: LZ77-like compression with fast random access. In: DCC, pp. 239–248. IEEE Computer Society (2010)
Kreft, S., Navarro, G.: On compressing and indexing repetitive sequences. Theor. Comput. Sci. 483, 115–133 (2013)
Mahoney, M.: Large text compression benchmark (2011)
Ziv, J., Lempel, A.: A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3), 337–343 (1977)
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Gawrychowski, P., Kosche, M., Manea, F. (2023). On the Number of Factors in the LZ-End Factorization. In: Nardini, F.M., Pisanti, N., Venturini, R. (eds) String Processing and Information Retrieval. SPIRE 2023. Lecture Notes in Computer Science, vol 14240. Springer, Cham. https://doi.org/10.1007/978-3-031-43980-3_20
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