Research output per year
Research output per year
Ilan Newman, Yuri Rabinovich, Deepak Rajendraprasad, Christian Sohler
Research output: Contribution to journal āŗ Article āŗ peer-review
A sequence f ā¶ [n] ā R contains a pattern š ĻāS_{k}, that is, a permutations of [k], iff there are indices i_{1} < ā¦ < i_{k}, such that f(i_{x}) > f(i_{y}) whenever Ļ(x) > Ļ(y). Otherwise, f is Ļ-free. We study the property testing problem of distinguishing, for a fixed Ļ, between Ļ-free sequences and the sequences which differ from any Ļ-free sequence in more than Ļµ n places. Our main findings are as follows: (1) For monotone patterns, that is, Ļ = (k,k ā 1,ā¦,1) and Ļ = (1,2,ā¦,k), there exists a nonadaptive one-sided error Ļµ-test of (Ļµšā1 log n)O(k^{2}) query complexity. For any other Ļ, any nonadaptive one-sided error test requires Ī©(ān) queries. The latter lower-bound is tight for Ļ = (1,3,2). For specific ĻāS_{k} it can be strengthened to Ī©(n^{1 ā 2/(k + 1)}). The general case upper-bound is O(Ļµ^{ā1/k}n^{1 ā 1/k}). (2) For adaptive testing the situation is quite different. In particular, for any ĻāS_{3} there exists an adaptive Ļµ-tester of (Ļµšā1 log n)O^{(1)} query complexity.
Original language | English |
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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 āŗ Conference contribution āŗ peer-review