Asymptotically Optimal Randomized Rumor Spreading

TL;DR

This paper introduces an asymptotically optimal randomized rumor spreading protocol that efficiently disseminates information to all nodes using only push operations, achieving near-optimal time and call complexity.

Contribution

It presents the first randomized push protocol that attains asymptotically optimal spreading time of (1 + o(1)) log₂ n with only push operations.

Findings

Spreads rumor in asymptotically optimal time of (1 + o(1)) log₂ n.

Uses only push operations, simplifying implementation.

Achieves O(n f(n)) calls with arbitrary ω(1) function f(n).

Abstract

We propose a new protocol solving the fundamental problem of disseminating a piece of information to all members of a group of n players. It builds upon the classical randomized rumor spreading protocol and several extensions. The main achievements are the following: Our protocol spreads the rumor to all other nodes in the asymptotically optimal time of (1 + o(1)) \log_2 n. The whole process can be implemented in a way such that only O(n f(n)) calls are made, where f(n)= \omega(1) can be arbitrary. In contrast to other protocols suggested in the literature, our algorithm only uses push operations, i.e., only informed nodes take active actions in the network. To the best of our knowledge, this is the first randomized push algorithm that achieves an asymptotically optimal running time.