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.2017.38
URN: urn:nbn:de:0030-drops-75877
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/7587/
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Chen, Xi ; Servedio, Rocco A. ; Tan, Li-Yang ; Waingarten, Erik

Adaptivity Is Exponentially Powerful for Testing Monotonicity of Halfspaces

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Abstract

We give a poly(log(n),1/epsilon)-query adaptive algorithm for testing whether an unknown Boolean function f:{-1, 1}^n -> {-1, 1}, which is promised to be a halfspace, is monotone versus epsilon-far from monotone. Since non-adaptive algorithms are known to require almost Omega(n^{1/2}) queries to test whether an unknown halfspace is monotone versus far from monotone, this shows that adaptivity enables an exponential improvement in the query complexity of monotonicity testing for halfspaces.

BibTeX - Entry

@InProceedings{chen_et_al:LIPIcs:2017:7587,
  author =	{Xi Chen and Rocco A. Servedio and Li-Yang Tan and Erik Waingarten},
  title =	{{Adaptivity Is Exponentially Powerful for Testing Monotonicity of Halfspaces}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)},
  pages =	{38:1--38:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-044-6},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{81},
  editor =	{Klaus Jansen and Jos{\'e} D. P. Rolim and David Williamson and Santosh S. Vempala},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7587},
  URN =		{urn:nbn:de:0030-drops-75877},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2017.38},
  annote =	{Keywords: property testing, linear threshold functions, monotonicity, adaptivity}
}

Keywords: property testing, linear threshold functions, monotonicity, adaptivity
Collection: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)
Issue Date: 2017
Date of publication: 11.08.2017

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