Testing odd direct sums using high dimensional expanders

Roy Gotlib, Tali Kaufman

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

3 Scopus citations

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 [9] 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.

Original languageEnglish
Title of host publicationApproximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2019
EditorsDimitris Achlioptas, Laszlo A. Vegh
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771252
DOIs
StatePublished - Sep 2019
Event22nd International Conference on Approximation Algorithms for Combinatorial Optimization Problems and 23rd International Conference on Randomization and Computation, APPROX/RANDOM 2019 - Cambridge, United States
Duration: 20 Sep 201922 Sep 2019

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume145
ISSN (Print)1868-8969

Conference

Conference22nd International Conference on Approximation Algorithms for Combinatorial Optimization Problems and 23rd International Conference on Randomization and Computation, APPROX/RANDOM 2019
Country/TerritoryUnited States
CityCambridge
Period20/09/1922/09/19

Bibliographical note

Publisher Copyright:
© Roy Gotlib and Tali Kaufman.

Keywords

  • Direct Sum
  • High Dimensional Expanders
  • Property Testing

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