Strongly Sublinear Algorithms for Testing Pattern Freeness

Ilan Newman, Nithin Varma

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

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 languageEnglish
Title of host publication49th EATCS International Conference on Automata, Languages, and Programming, ICALP 2022
EditorsMikolaj Bojanczyk, Emanuela Merelli, David P. Woodruff
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959772358
DOIs
StatePublished - 1 Jul 2022
Event49th EATCS International Conference on Automata, Languages, and Programming, ICALP 2022 - Paris, France
Duration: 4 Jul 20228 Jul 2022

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume229
ISSN (Print)1868-8969

Conference

Conference49th EATCS International Conference on Automata, Languages, and Programming, ICALP 2022
Country/TerritoryFrance
CityParis
Period4/07/228/07/22

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

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