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- W3209103818 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 $eps in (0,1), s in mathbb{N}$, and oracle access to a function, $eps$-tests convexity in $O(log (s)/eps)$, 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 $s leq n$, our query complexity bound is at least as good as that of the optimal convexity tester (Ben Eliezer; ITCS 2019) with complexity $O(frac{log eps n}{eps})$; 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 $Omega(frac{log (eps n)}{eps})$ expressed in terms of the input size and obtain a more efficient algorithm." @default.
- W3209103818 created "2021-11-08" @default.
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- W3209103818 date "2021-10-25" @default.
- W3209103818 modified "2023-09-27" @default.
- W3209103818 title "Parameterized Convexity Testing" @default.
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