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.ITCS.2017.33
URN: urn:nbn:de:0030-drops-81619
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/8161/
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Blais, Eric ; Bommireddi, Abhinav

Testing Submodularity and Other Properties of Valuation Functions

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LIPIcs-ITCS-2017-33.pdf (0.6 MB)

Abstract

We show that for any constant \epsilon > 0 and p \ge 1, it is possible to distinguish functions f : \{0,1\}^n \to [0,1] that are submodular from those that are \epsilon-far from every submodular function in \ell_p distance with a constant number of queries.

More generally, we extend the testing-by-implicit-learning framework of Diakonikolas et al.(2007) to show that every property of real-valued functions that is well-approximated in \ell_2 distance by a class of k-juntas for some k = O(1) can be tested in the \ell_p-testing model with a constant number of queries. This result, combined with a recent junta theorem of Feldman and \Vondrak (2016), yields the constant-query testability of submodularity. It also yields constant-query testing algorithms for a variety of other natural properties of valuation functions, including fractionally additive (XOS) functions, OXS functions, unit demand functions, coverage functions, and self-bounding functions.

BibTeX - Entry

@InProceedings{blais_et_al:LIPIcs:2017:8161,
  author =	{Eric Blais and Abhinav Bommireddi},
  title =	{{Testing Submodularity and Other Properties of Valuation Functions}},
  booktitle =	{8th Innovations in Theoretical Computer Science Conference (ITCS 2017)},
  pages =	{33:1--33:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-029-3},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{67},
  editor =	{Christos H. Papadimitriou},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/8161},
  URN =		{urn:nbn:de:0030-drops-81619},
  doi =		{10.4230/LIPIcs.ITCS.2017.33},
  annote =	{Keywords: Property testing, Testing by implicit learning, Self-bounding functions}
}

Keywords: Property testing, Testing by implicit learning, Self-bounding functions
Collection: 8th Innovations in Theoretical Computer Science Conference (ITCS 2017)
Issue Date: 2017
Date of publication: 28.11.2017

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