Random k-out subgraph leaves only O(n/k) inter-component edges

Jacob Holm, Valerie King, Mikkel Thorup, Or Zamir, Uri Zwick

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

Abstract

Each vertex of an arbitrary simple graph on n vertices chooses k random incident edges. What is the expected number of edges in the original graph that connect different connected components of the sampled subgraph? We prove that the answer is O(n/k), when k ≥ c log n, for some large enough c. We conjecture that the same holds for smaller values of k, possibly for any k ≥ 2. Such a result is best possible for any k ≥ 2. As an application, we use this sampling result to obtain a one-way communication protocol with private randomness for finding a spanning forest of a graph in which each vertex sends only O (√n log n) bits to a referee.

Original languageEnglish
Title of host publicationProceedings - 2019 IEEE 60th Annual Symposium on Foundations of Computer Science, FOCS 2019
PublisherIEEE Computer Society
Pages896-909
Number of pages14
ISBN (Electronic)9781728149523
DOIs
StatePublished - Nov 2019
Event60th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2019 - Baltimore, United States
Duration: 9 Nov 201912 Nov 2019

Publication series

NameProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
Volume2019-November
ISSN (Print)0272-5428

Conference

Conference60th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2019
Country/TerritoryUnited States
CityBaltimore
Period9/11/1912/11/19

Funding

FundersFunder number
Basic Algorithms Research Copenhagen
Blavatnik Computer Science Research Fund
VIL-LUM Foundation
Natural Sciences and Engineering Research Council of Canada

    Keywords

    • Connected components
    • Random subgraph
    • communication complexity

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