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- W4205362912 abstract "In this work, we develop new insights into the fundamental problem of convexity testing of real-valued functions over the domain [n]. Specifically, we present a nonadaptive algorithm that, given inputs ε ∊ (0,1), s ∊ ℕ, and oracle access to a function, ε-tests convexity in O(log(s)/ε), where s is an upper bound on the number of distinct discrete derivatives of the function. We also show that this bound is tight. Since s ≤ n, our query complexity bound is at least as good as that of the optimal convexity tester (Ben Eliezer; ITCS 2019) with complexity ; our bound is strictly better when s = o(n). The main contribution of our work is to appropriately parameterize the complexity of convexity testing to circumvent the worst-case lower bound (Belovs et al.; SODA 2020) of expressed in terms of the input size and obtain a more efficient algorithm." @default.
- W4205362912 created "2022-01-25" @default.
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- W4205362912 date "2022-01-01" @default.
- W4205362912 modified "2023-09-23" @default.
- W4205362912 title "Parameterized Convexity Testing" @default.
- W4205362912 doi "https://doi.org/10.1137/1.9781611977066.12" @default.
- W4205362912 hasPublicationYear "2022" @default.
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