An Optimal Lower Bound for Monotonicity Testing over Hypergrids
An Optimal Lower Bound for Monotonicity Testing over Hypergrids
复制标题
超网格单调性测试的最佳下界
作者：
Elena Grigorescu;Karl Wimmer;Alan Guo;R. Rubinfeld;Uri Stemmer;Janardhan Kulkarni;Benjamin Moseley;Adi Rosen
对于正整数n，d，考虑超网格[n] d，其坐标乘积偏序记为n。一个函数f：[n] d → n是单调的，如果n x <$y，f（x）≤ f（y）.一个函数f是e-远离单调的，如果至少一个e-分数的值必须改变，使f单调。给定一个参数e，单调性测试者必须以高概率区分单调函数和e-far函数。
For positive integers n, d, consider the hypergrid [n] d with the coordinate-wise product partial ordering denoted by ≺. A function f: [n] d → ℕ is monotone if ∀ x ≺ y, f(x) ≤ f(y). A function f is e-far from monotone if at least an e-fraction of values must be changed to make f monotone. Given a parameter e, a monotonicity tester must distinguish with high probability a monotone function from one that is e-far.