Abstract
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], 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 f differs on at least εn values from every π-free function. This is a generalization of the well-studied monotonicity testing and was first studied by Newman, Rabinovich, Rajendraprasad and Sohler [28]. We show that for all constants k ∈ N, ε ∈ (0, 1), and permutation π : [k] → [k], there is a one-sided error ε-testing algorithm for π-freeness of functions f : [n] → R that makes Õ(no(1)) queries. We improve significantly upon the previous best upper bound O(n1−1/(k−1)) by Ben-Eliezer and Canonne [7]. Our algorithm is adaptive, while the earlier best upper bound is known to be tight for nonadaptive algorithms.
Original language | English |
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Title of host publication | 49th EATCS International Conference on Automata, Languages, and Programming, ICALP 2022 |
Editors | Mikolaj Bojanczyk, Emanuela Merelli, David P. Woodruff |
Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |
ISBN (Electronic) | 9783959772358 |
DOIs | |
State | Published - 1 Jul 2022 |
Event | 49th EATCS International Conference on Automata, Languages, and Programming, ICALP 2022 - Paris, France Duration: 4 Jul 2022 → 8 Jul 2022 |
Publication series
Name | Leibniz International Proceedings in Informatics, LIPIcs |
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Volume | 229 |
ISSN (Print) | 1868-8969 |
Conference
Conference | 49th EATCS International Conference on Automata, Languages, and Programming, ICALP 2022 |
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Country/Territory | France |
City | Paris |
Period | 4/07/22 → 8/07/22 |
Bibliographical note
Publisher Copyright:© Ilan Newman and Nithin Varma; licensed under Creative Commons License CC-BY 4.0
Keywords
- Pattern freeness
- Property testing
- Sublinear algorithms
ASJC Scopus subject areas
- Software