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The sensitivity of a string compression algorithm C asks how much the output size C(T ) for an input string T can increase when a single character edit operation is performed on T . This notion enables one to measure the robustness of compression algorithms in terms of errors and/or dynamic changes occurring in the input string.In this paper, we analyze the worst-case multiplicative sensitivity of string compression algorithms, which is defined by max T ∈Σ n {C(T )/C(T ) : ed(T, T ) = 1}, where ed(T, T ) denotes the edit distance between T and T . In particular, for the most common versions of the Lempel-Ziv 77 compressors, we prove that the worst-case multiplicative sensitivity is only a small constant (2 or 3, depending on the version of the Lempel-Ziv 77 and the edit operation type), i.e., the size z of the Lempel-Ziv 77 factorizations can be larger by only a small constant factor. We strengthen our upper bound results by presenting matching lower bounds on the worst-case sensitivity for all these major versions of the Lempel-Ziv 77 factorizations. This contrasts with the previously known related results such that the size z 78 of the Lempel-Ziv 78 factorization can increase by a factor of Ω(n 3/4 ) [Lagarde and Perifel, 2018], and the number r of runs in the Burrows-Wheeler transform can increase by a factor of Ω(log n) [Giuliani et al., 2021] when a character is prepended to an input string of length n. We also study the worst-case sensitivity of several grammar compression algorithms including Bisection, AVL-grammar, GCIS (Grammar Compression by Induced Sorting), and CDAWG (Compact Directed Acyclic Word Graph). Further, we extend the notion of the worst-case sensitivity to string repetitiveness measures such as the smallest string attractor size γ and the substring complexity δ, and present matching upper and lower bounds of the worst-case multiplicative sensitivity for γ and δ. We also exhibit the worst-case additive sensitivity max T ∈Σ n {C(T ) − C(T ) : ed(T, T ) = 1}, which allows one to observe more details in the changes of the output sizes.

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