
Encoding twodimensional range topk queries revisited
We consider the problem of encoding twodimensional arrays, whose elemen...
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Reply to Chen et al.: Parametric methods for cluster inference perform worse for twosided ttests
Onesided ttests are commonly used in the neuroimaging field, but twos...
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Boolean Unateness Testing with O(n^3/4) Adaptive Queries
We give an adaptive algorithm which tests whether an unknown Boolean fun...
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Lower Bounds for Tolerant Junta and Unateness Testing via Rejection Sampling of Graphs
We introduce a new model for testing graph properties which we call the ...
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Discriminative Learning via Adaptive Questioning
We consider the problem of designing an adaptive sequence of questions t...
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An Optimal Tester for kLinear
A Boolean function f:{0,1}^n→{0,1} is klinear if it returns the sum (ov...
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Strongly Sublinear Algorithms for Testing Pattern Freeness
Given a permutation π:[k] → [k], a function f:[n] →ℝ contains a πappear...
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Improved Bounds for Testing Forbidden Order Patterns
A sequence f{1,...,n}→R contains a permutation π of length k if there exist i_1<...<i_k such that, for all x,y, f(i_x)<f(i_y) if and only if π(x)<π(y); otherwise, f is said to be πfree. In this work, we consider the problem of testing for πfreeness with onesided error, continuing the investigation of [Newman et al., SODA'17]. We demonstrate a surprising behavior for nonadaptive tests with onesided error: While a trivial samplingbased approach yields an εtest for πfreeness making Θ(ε^1/k n^11/k) queries, our lower bounds imply that this is almost optimal for most permutations! Specifically, for most permutations π of length k, any nonadaptive onesided εtest requires ε^1/(kΘ(1))n^11/(kΘ(1)) queries; furthermore, the permutations that are hardest to test require Θ(ε^1/(k1)n^11/(k1)) queries, which is tight in n and ε. Additionally, we show two hierarchical behaviors here. First, for any k and l≤ k1, there exists some π of length k that requires Θ̃_ε(n^11/l) nonadaptive queries. Second, we show an adaptivity hierarchy for π=(1,3,2) by proving upper and lower bounds for (one and twosided) testing of πfreeness with r rounds of adaptivity. The results answer open questions of Newman et al. and [Canonne and Gur, CCC'17].
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