Papers › On Two LZ78-style Grammars: Compression Bounds and Compressed-Space Computation
On Two LZ78-style Grammars: Compression Bounds and Compressed-Space Computation
Golnaz Badkobeh, Travis Gagie, Shunsuke Inenaga, Tomasz Kociumaka, Dmitry Kosolobov, Simon J. Puglisi
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We investigate two closely related LZ78-based compression schemes: LZMW (an old scheme by Miller and Wegman) and LZD (a recent variant by Goto et al.). Both LZD and LZMW naturally produce a grammar for a string of length n; we show that the size of this grammar can be larger than the size of the smallest grammar by a factor Ω(n^(1/3)) but is always within a factor O((n/logn)^(2/3)). In addition, we show that the standard algorithms using Θ(z) working space to construct the LZD and LZMW parsings, where z is the size of the parsing, work in Ω(n^(5/4)) time in the worst case. We then describe a new Las Vegas LZD/LZMW parsing algorithm that uses O (z logn) space and O(n + z log² n) time w.h.p..
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