Research output per year
Research output per year
Ilan Newman, Yuri Rabinovich, Deepak Rajendraprasad, Christian Sohler
Research output: Contribution to journal › Article › peer-review
A sequence f ∶ [n] → R contains a pattern 𝜋 π∈S_{k}, that is, a permutations of [k], iff there are indices i_{1} < … < i_{k}, such that f(i_{x}) > f(i_{y}) whenever π(x) > π(y). Otherwise, f is π-free. We study the property testing problem of distinguishing, for a fixed π, between π-free sequences and the sequences which differ from any π-free sequence in more than ϵ n places. Our main findings are as follows: (1) For monotone patterns, that is, π = (k,k − 1,…,1) and π = (1,2,…,k), there exists a nonadaptive one-sided error ϵ-test of (ϵ𝜖−1 log n)O(k^{2}) query complexity. For any other π, any nonadaptive one-sided error test requires Ω(√n) queries. The latter lower-bound is tight for π = (1,3,2). For specific π∈S_{k} it can be strengthened to Ω(n^{1 − 2/(k + 1)}). The general case upper-bound is O(ϵ^{−1/k}n^{1 − 1/k}). (2) For adaptive testing the situation is quite different. In particular, for any π∈S_{3} there exists an adaptive ϵ-tester of (ϵ𝜖−1 log n)O^{(1)} query complexity.
Original language | English |
---|---|
Pages (from-to) | 402-426 |
Number of pages | 25 |
Journal | Random Structures and Algorithms |
Volume | 55 |
Issue number | 2 |
DOIs | |
State | Published - Sep 2019 |
Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review