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Breaking the \(\log n\) barrier on rumor spreading

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Abstract

\(O(\log n)\) rounds has been a well known upper bound for rumor spreading using push&pull in the random phone call model (i.e., uniform gossip in the complete graph). A matching lower bound of \(\varOmega (\log n)\) is also known for this special case. Under the assumption of this model and with a natural addition that nodes can call a partner once they learn its address (e.g., its IP address) we present a new distributed, address-oblivious and robust algorithm that uses push&pull with pointer jumping to spread a rumor to all nodes in only \(O(\sqrt{\log n})\) rounds, w.h.p. This algorithm can also cope with \(F= O(n/2^{\sqrt{\log n}})\) node failures, in which case all but O(F) nodes become informed within \(O(\sqrt{\log n})\) rounds, w.h.p.

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Notes

  1. In this paper with high probably or w.h.p. is with probability at least \(1-n^{-1-\varOmega (1)}\).

  2. A call, in which no data is sent (e.g., the rumor, or a pointer), is not considered as a message.

  3. Note that in [23] the authors consider arbitrary node weights, which are 1 / n for all nodes in our case.

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Authors and Affiliations

  1. Communication Systems Engineering, Ben Gurion University of the Negev, Beer-Sheva, Israel

    Chen Avin

  2. Department of Computer Sciences, University of Salzburg, Salzburg, Austria

    Robert Elsässer

Authors
  1. Chen Avin
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  2. Robert Elsässer
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Correspondence to Chen Avin.

Additional information

An extended abstract of this work appeared in [1]. The work of the second author was partially supported by the Austrian Science Fund (FWF) under contract P25214-N23 “Analysis of Epidemic Processes and Algorithms in Large Networks”. The main result of this paper solves an open problem presented at Dagstuhl Seminar 13042 “Epidemic Algorithms and Processes: From Theory to Applications”.

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Avin, C., Elsässer, R. Breaking the \(\log n\) barrier on rumor spreading. Distrib. Comput. 31, 503–513 (2018). https://doi.org/10.1007/s00446-017-0312-4

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