research-article

On the Sensitivity Complexity of k-Uniform Hypergraph Properties

Authors:

Xiaoming SunAuthors Info & Claims

ACM Transactions on Computation Theory (TOCT), Volume 13, Issue 2

Article No.: 12, Pages 1 - 13

https://doi.org/10.1145/3448643

Published: 26 March 2021 Publication History

Abstract

In this article, we investigate the sensitivity complexity of hypergraph properties. We present a k-uniform hypergraph property with sensitivity complexity O(n(⌈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⌈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 Ω (n^k/2). We also investigate the sensitivity complexity of other symmetric functions and show that for many classes of transitive Boolean functions the minimum achievable sensitivity complexity can be O(N^1/3), where N is the number of variables.

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Cited By

Gu KGrunde-McLaughlin MMcNutt AHeer JAlthoff T(2024)How Do Data Analysts Respond to AI Assistance? A Wizard-of-Oz StudyProceedings of the 2024 CHI Conference on Human Factors in Computing Systems10.1145/3613904.3641891(1-22)Online publication date: 11-May-2024
https://dl.acm.org/doi/10.1145/3613904.3641891
Cheng FCui JWang QZhang L(2023)A Variable Granularity Search-Based Multiobjective Feature Selection Algorithm for High-Dimensional Data ClassificationIEEE Transactions on Evolutionary Computation10.1109/TEVC.2022.316045827:2(266-280)Online publication date: 1-Apr-2023
https://dl.acm.org/doi/10.1109/TEVC.2022.3160458
Csernák TSoukup L(2023)Elusive properties of infinite graphsJournal of Graph Theory10.1002/jgt.23042105:3(427-450)Online publication date: 26-Oct-2023
https://doi.org/10.1002/jgt.23042

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Published In

cover image ACM Transactions on Computation Theory

ACM Transactions on Computation Theory Volume 13, Issue 2

June 2021

144 pages

ISSN:1942-3454

EISSN:1942-3462

DOI:10.1145/3450495

Editor:
Ryan O'Donnell
Carnegie Mellon University, USA

Issue’s Table of Contents

Copyright © 2021 ACM.

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Publication History

Published: 26 March 2021

Accepted: 01 January 2021

Revised: 01 December 2020

Received: 01 September 2019

Published in TOCT Volume 13, Issue 2

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National Natural Science Foundation of China
Strategic Priority Research Program of Chinese Academy of Sciences
973 Program of China

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Cited By

Gu KGrunde-McLaughlin MMcNutt AHeer JAlthoff T(2024)How Do Data Analysts Respond to AI Assistance? A Wizard-of-Oz StudyProceedings of the 2024 CHI Conference on Human Factors in Computing Systems10.1145/3613904.3641891(1-22)Online publication date: 11-May-2024
https://dl.acm.org/doi/10.1145/3613904.3641891
Cheng FCui JWang QZhang L(2023)A Variable Granularity Search-Based Multiobjective Feature Selection Algorithm for High-Dimensional Data ClassificationIEEE Transactions on Evolutionary Computation10.1109/TEVC.2022.316045827:2(266-280)Online publication date: 1-Apr-2023
https://dl.acm.org/doi/10.1109/TEVC.2022.3160458
Csernák TSoukup L(2023)Elusive properties of infinite graphsJournal of Graph Theory10.1002/jgt.23042105:3(427-450)Online publication date: 26-Oct-2023
https://doi.org/10.1002/jgt.23042

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