Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sensitivity of string compressors and repetitiveness measures   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, defined by
$\max_{T \in \Sigma^n}\{C(T')/C(T) : ed(T, T') = 1\}$, where $ed(T, T')$
denotes the edit distance between $T$ and $T'$. 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). 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 $z_{\rm 78}$ of
the Lempel-Ziv 78 factorization can increase by a factor of $\Omega(n^{1/4})$
[Lagarde and Perifel, 2018], and the number $r$ of runs in the Burrows-Wheeler
transform can increase by a factor of $\Omega(\log n)$ [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, and CDAWG. Further, we extend the notion of the
worst-case sensitivity to string repetitiveness measures such as the smallest
string attractor size $\gamma$ and the substring complexity $\delta$. We
present some non-trivial upper and lower bounds of the worst-case
multiplicative sensitivity for $\gamma$ and matching upper and lower bounds of
the worst-case multiplicative sensitivity for $\delta$.

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The categories of this paper are: physics
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The categories of this paper are: nlin
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The categories of this paper are: hep-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: econ
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: funct-an
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The categories of this paper are: hep-th
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: gr-qc
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The categories of this paper are: cond-mat