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Relations Between Greedy and Bit-Optimal LZ77 Encodings Kosolobov, Dmitry Lempel-Ziv LZ77 encoding greedy LZ77 bit optimal LZ77 This paper investigates the size in bits of the LZ77 encoding, which is the most popular and efficient variant of the Lempel-Ziv encodings used in data compression. We prove that, for a wide natural class of variable-length encoders for LZ77 phrases, the size of the greedily constructed LZ77 encoding on constant alphabets is within a factor O(log n / log log log n) of the optimal LZ77 encoding, where n is the length of the processed string. We describe a series of examples showing that, surprisingly, this bound is tight, thus improving both the previously known upper and lower bounds. Further, we obtain a more detailed bound O(min{z, log n / log log z}), which uses the number z of phrases in the greedy LZ77 encoding as a parameter, and construct a series of examples showing that this bound is tight even for binary alphabet. We then investigate the problem on non-constant alphabets: we show that the known O(log n) bound is tight even for alphabets of logarithmic size, and provide tight bounds for some other important cases. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Dmitry Kosolobov 2018 Is Part Of LIPIcs, Volume 96, 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.STACS.2018.46 urn:nbn:de:0030-drops-84894 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2018.46 eng https://creativecommons.org/licenses/by/3.0/legalcode