Strongly Sublinear Algorithms for Testing Pattern Freeness

  title={Strongly Sublinear Algorithms for Testing Pattern Freeness},
  author={Ilan Newman and Nithin M. Varma},
For a permutation π : [k] → [k], a function f : [n] → R contains a π-appearance if there exists 1 ≤ i1 < i2 < · · · < ik ≤ n such that for all s, t ∈ [k], it holds that f(is) < f(it) if and only if π(s) < π(t). The function is π-free if it has no π-appearances. In this paper, we investigate the problem of testing whether an input function f is π-free or whether at least εn values in f need to be changed in order to make it π-free. This problem is a generalization of the well-studied… 

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