License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2020.27
URN: urn:nbn:de:0030-drops-126307
URL: https://drops.dagstuhl.de/opus/volltexte/2020/12630/
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Ron, Dana ; Rosin, Asaf

Almost Optimal Distribution-Free Sample-Based Testing of k-Modality

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LIPIcs-APPROX27.pdf (0.6 MB)

Abstract

For an integer k ≥ 0, a sequence σ = σ₁,… ,σ_n over a fully ordered set is k-modal, if there exist indices 1 = a₀ < a₁ < … < a_{k+1} = n such that for each i, the subsequence σ_{a_i},… ,σ_{a_{i+1}} is either monotonically non-decreasing or monotonically non-increasing. The property of k-modality is a natural extension of monotonicity, which has been studied extensively in the area of property testing. We study one-sided error property testing of k-modality in the distribution-free sample-based model. We prove an upper bound of O({√{kn}log k}/ε) on the sample complexity, and an almost matching lower bound of Ω(√{kn}/ε). When the underlying distribution is uniform, we obtain a completely tight bound of Θ(√{kn/ε}), which generalizes what is known for sample-based testing of monotonicity under the uniform distribution.

BibTeX - Entry

@InProceedings{ron_et_al:LIPIcs:2020:12630,
  author =	{Dana Ron and Asaf Rosin},
  title =	{{Almost Optimal Distribution-Free Sample-Based Testing of k-Modality}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)},
  pages =	{27:1--27:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-164-1},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{176},
  editor =	{Jaros{\l}aw Byrka and Raghu Meka},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12630},
  URN =		{urn:nbn:de:0030-drops-126307},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2020.27},
  annote =	{Keywords: Sample-based property testing, Distribution-free property testing, k-modality}
}

Keywords: Sample-based property testing, Distribution-free property testing, k-modality
Collection: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)
Issue Date: 2020
Date of publication: 11.08.2020

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