Efficient information exchange in the random phone-call model

Petra Berenbrink, Jurek Czyzowicz, Robert Elsässer, Leszek Ga̧sieniec

Research output: Chapter in Book/Report/Conference proceedingConference contribution

8 Scopus citations

Abstract

We consider the gossiping problem in the classical random phone-call model introduced by Demers et. al. ([6]). We are given a complete graph, in which every node has an initial message to be disseminated to all other nodes. In each step every node is allowed to establish a communication channel with a randomly chosen neighbour. Karp et al. [15] proved that it is possible to design a randomized procedure performing O(nloglogn) transmissions that accomplishes broadcasting in time O(logn), with probability 1-n -1. In this paper we provide a lower bound argument that proves Ω(nlogn) message complexity for any O(logn)-time randomized gossiping algorithm, with probability 1-o(1). This should be seen as a separation result between broadcasting and gossiping in the random phone-call model. We study gossiping at the two opposite points of the time and message complexity trade-off. We show that one can perform gossiping based on exchange of O(n•logn/loglogn) messages in time O(log2 n/loglogn), and based on exchange of O(nloglogn) messages with the time complexity Both results hold wit probability 1-n -1. Finally, we consider a model in which each node is allowed to store a small set of neighbours participating in its earlier transmissions. We show that in this model randomized gossiping based on exchange of O(nloglogn) messages can be obtained in time O(logn), with probability 1-n -1.

Original languageEnglish (US)
Title of host publicationAutomata, Languages and Programming - 37th International Colloquium, ICALP 2010, Proceedings
Pages127-138
Number of pages12
EditionPART 2
DOIs
StatePublished - Aug 12 2010
Externally publishedYes
Event37th International Colloquium on Automata, Languages and Programming, ICALP 2010 - Bordeaux, France
Duration: Jul 6 2010Jul 10 2010

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 2
Volume6199 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference37th International Colloquium on Automata, Languages and Programming, ICALP 2010
CountryFrance
CityBordeaux
Period7/6/107/10/10

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Berenbrink, P., Czyzowicz, J., Elsässer, R., & Ga̧sieniec, L. (2010). Efficient information exchange in the random phone-call model. In Automata, Languages and Programming - 37th International Colloquium, ICALP 2010, Proceedings (PART 2 ed., pp. 127-138). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6199 LNCS, No. PART 2). https://doi.org/10.1007/978-3-642-14162-1_11