Strong Robustness of Randomized Rumor Spreading Protocols

TL;DR

This paper analyzes the robustness of quasirandom rumor spreading protocols in complete networks, showing they are nearly as resilient as fully random protocols under transmission failures with precise run-time bounds.

Contribution

It provides a detailed, tight analysis of the quasirandom rumor spreading protocol's robustness, including exact run-time bounds under transmission failures.

Findings

Quasirandom protocol remains robust with near-optimal run-time under transmission failures.

Run-time increases by a factor related to transmission success probability p.

Lower bounds confirm the quasirandom protocol's robustness matches that of fully random protocols.

Abstract

Randomized rumor spreading is a classical protocol to disseminate information across a network. At SODA 2008, a quasirandom version of this protocol was proposed and competitive bounds for its run-time were proven. This prompts the question: to what extent does the quasirandom protocol inherit the second principal advantage of randomized rumor spreading, namely robustness against transmission failures? In this paper, we present a result precise up to $(1 \pm o(1))$ factors. We limit ourselves to the network in which every two vertices are connected by a direct link. Run-times accurate to their leading constants are unknown for all other non-trivial networks. We show that if each transmission reaches its destination with a probability of $p \in (0,1]$, after $(1+\e)(\frac{1}{\log_2(1+p)}\log_2n+\frac{1}{p}\ln n)$ rounds the quasirandom protocol has informed all $n$ nodes in the network with probability at least $1-n^{-p\e/40}$. Note that this is faster than the intuitively natural $1/p$ factor increase over the run-time of approximately $\log_2 n + \ln n $ for the non-corrupted case. We also provide a corresponding lower bound for the classical model. This demonstrates that the quasirandom model is at least as robust as the fully random model despite the greatly reduced degree of independent randomness.