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- W4386870791 abstract "In this paper we extend to two-dimensional data two recently introduced one-dimensional compressibility measures: the $$gamma $$ measure defined in terms of the smallest string attractor, and the $$delta $$ measure defined in terms of the number of distinct substrings of the input string. Concretely, we introduce the two-dimensional measures $$gamma _{2D}$$ and $$delta _{2D}$$ as natural generalizations of $$gamma $$ and $$delta $$ and study some of their properties. Among other things, we prove that $$delta _{2D}$$ is monotone and can be computed in linear time, and we show that although it is still true that $$delta _{2D}le gamma _{2D}$$ the gap between the two measures can be $$varOmega (sqrt{n})$$ for families of $$ntimes n$$ matrices and therefore asymptotically larger than the gap in one-dimension. Finally, we use the measures $$gamma _{2D}$$ and $$delta _{2D}$$ to provide the first analysis of the space usage of the two-dimensional block tree introduced in [Brisaboa et al., Two-dimensional block trees, The computer Journal, 2023]." @default.
- W4386870791 created "2023-09-20" @default.
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- W4386870791 date "2023-01-01" @default.
- W4386870791 modified "2023-09-27" @default.
- W4386870791 title "Compressibility Measures for Two-Dimensional Data" @default.
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- W4386870791 doi "https://doi.org/10.1007/978-3-031-43980-3_9" @default.
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