An Optimal Lower Bound for Monotonicity Testing over Hypergrids

  title={An Optimal Lower Bound for Monotonicity Testing over Hypergrids},
  author={Deeparnab Chakrabarty and C. Seshadhri},
  journal={Electron. Colloquium Comput. Complex.},
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. 
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