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.STACS.2017.51
URN: urn:nbn:de:0030-drops-69825
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/6982/
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Li, Qian ; Sun, Xiaoming

On the Sensitivity Complexity of k-Uniform Hypergraph Properties

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LIPIcs-STACS-2017-51.pdf (0.5 MB)

Abstract

In this paper we investigate the sensitivity complexity of hypergraph properties. We present a k-uniform hypergraph property with sensitivity complexity O(n^{ceil(k/3)}) for any k >= 3, where n is the number of vertices. Moreover, we can do better when k = 1 (mod 3) by presenting a k-uniform hypergraph property with sensitivity O(n^{ceil(k/3)-1/2}). This result disproves a conjecture of Babai, which conjectures that the sensitivity complexity of k-uniform hypergraph properties is at least Omega(n^{k/2}). We also investigate the sensitivity complexity of other weakly symmetric functions and show that for many classes of transitive-invariant Boolean functions the minimum achievable sensitivity complexity can be O(N^{1/3}), where N is the number of variables. Finally, we give a lower bound for sensitivity of k-uniform hypergraph properties, which implies the sensitivity conjecture of k-uniform hypergraph properties for any constant k.

BibTeX - Entry

@InProceedings{li_et_al:LIPIcs:2017:6982,
  author =	{Qian Li and Xiaoming Sun},
  title =	{{On the Sensitivity Complexity of k-Uniform Hypergraph Properties}},
  booktitle =	{34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)},
  pages =	{51:1--51:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-028-6},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{66},
  editor =	{Heribert Vollmer and Brigitte ValleĢe},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/6982},
  URN =		{urn:nbn:de:0030-drops-69825},
  doi =		{10.4230/LIPIcs.STACS.2017.51},
  annote =	{Keywords: Sensitivity Complexity, k-uniform Hypergraph Properties, Boolean Function, Turan's question}
}

Keywords: Sensitivity Complexity, k-uniform Hypergraph Properties, Boolean Function, Turan's question
Collection: 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)
Issue Date: 2017
Date of publication: 06.03.2017

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