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.2019.50
URN: urn:nbn:de:0030-drops-112651
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/11265/
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Gotlib, Roy ; Kaufman, Tali

Testing Odd Direct Sums Using High Dimensional Expanders

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LIPIcs-APPROX-RANDOM-2019-50.pdf (0.5 MB)

Abstract

In this work, using methods from high dimensional expansion, we show that the property of k-direct-sum is testable for odd values of k . Previous work of [Kaufman and Lubotzky, 2014] could inherently deal only with the case that k is even, using a reduction to linearity testing. Interestingly, our work is the first to combine the topological notion of high dimensional expansion (called co-systolic expansion) with the combinatorial/spectral notion of high dimensional expansion (called colorful expansion) to obtain the result.
The classical k-direct-sum problem applies to the complete complex; Namely it considers a function defined over all k-subsets of some n sized universe. Our result here applies to any collection of k-subsets of an n-universe, assuming this collection of subsets forms a high dimensional expander.

BibTeX - Entry

@InProceedings{gotlib_et_al:LIPIcs:2019:11265,
  author =	{Roy Gotlib and Tali Kaufman},
  title =	{{Testing Odd Direct Sums Using High Dimensional Expanders}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)},
  pages =	{50:1--50:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-125-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{145},
  editor =	{Dimitris Achlioptas and L{\'a}szl{\'o} A. V{\'e}gh},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/11265},
  URN =		{urn:nbn:de:0030-drops-112651},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2019.50},
  annote =	{Keywords: High Dimensional Expanders, Property Testing, Direct Sum}
}

Keywords: High Dimensional Expanders, Property Testing, Direct Sum
Collection: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)
Issue Date: 2019
Date of publication: 17.09.2019

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