Multi-Party Set Disjointness and Intersection with Bounded Dependence

Mark Braverman, Rotem Oshman, Tal Roth*

*Corresponding author for this work

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

Abstract

In the multi-party set disjointness problem, k players receive private inputs in the form of sets X1, ..., Xk ⊆ [n], and their goal is to check whether their sets intersect. The set intersection problem is similar, except that the players are required to output the full intersection of their sets rather than just checking whether it is empty. We study the communication complexity of these two problems in the shared-blackboard model of communication complexity, where players communicate with one another by broadcast.Set disjointness and set intersection are two of the most well-studied problems in communication complexity. It has long been known that two-party set disjointness is significantly easier when the players' inputs are independent of one another, and similar results have recently been established for multi-party set disjointness and intersection; however, these results do not apply when the players' inputs have even a small amount of dependence. In this work we close this gap, and give nearly-tight upper and lower bounds for set disjointness and set intersection as a function of the amount of dependence between the players' inputs. Our work explores two existing notions of correlation between the inputs to a multi-party communication protocol, total correlation and dual total correlation, and shows how each is useful in deriving lower and upper bounds, respectively.

Original languageEnglish
Title of host publicationPODC 2024 - Proceedings of the 2024 ACM Symposium on Principles of Distributed Computing
PublisherAssociation for Computing Machinery
Pages332-342
Number of pages11
ISBN (Electronic)9798400706684
DOIs
StatePublished - 17 Jun 2024
Event43rd ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, PODC 2024 - Nantes, France
Duration: 17 Jun 202421 Jun 2024

Publication series

NameProceedings of the Annual ACM Symposium on Principles of Distributed Computing

Conference

Conference43rd ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, PODC 2024
Country/TerritoryFrance
CityNantes
Period17/06/2421/06/24

Funding

FundersFunder number
NSF1933331
Israel Science Foundation2801/20

    Keywords

    • communication protocols
    • correlation
    • set disjointness
    • set intersection

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