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arXiv · 2506.22778

Tight Additive Sensitivity on LZ-style Compressors and String Attractors

Yuto Fujie·Hiroki Shibata·Yuto Nakashima·Shunsuke Inenaga
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Abstract

The worst-case additive sensitivity of a string repetitiveness measure $c$ is defined to be the largest difference between $c(w)$ and $c(w')$, where $w$ is a string of length $n$ and $w'$ is a string that can be obtained by performing a single-character edit operation on $w$. We present $O(\sqrt{n})$ upper bounds for the worst-case additive sensitivity of the smallest string attractor size $\gamma$ and the smallest bidirectional scheme size $b$, which match the known lower bounds $\Omega(\sqrt{n})$ for $\gamma$ and $b$ [Akagi et al. 2023]. Further, we present matching upper and lower bounds for the worst-case additive sensitivity of the Lempel-Ziv family - $\Theta(n^{\frac{2}{3}})$ for LZSS and LZ-End, and $\Theta(n)$ for LZ78.

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Yuto Fujie, Hiroki Shibata, Yuto Nakashima, Shunsuke Inenaga. 2025-06-28. Tight Additive Sensitivity on LZ-style Compressors and String Attractors. https://arxiv.org/abs/2506.22778

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