Gossip in a Smartphone Peer-to-Peer Network

TL;DR

This paper investigates gossip algorithms in a mobile peer-to-peer network model tailored for smartphones, analyzing their efficiency under dynamic topologies and limited communication, and introduces new algorithms with proven performance bounds.

Contribution

It introduces and analyzes new randomized gossip algorithms for the mobile telephone model, including solutions with and without shared randomness, and improves understanding of gossip in dynamic and stable networks.

Findings

Significant time complexity gap based on bit advertisement capability.

Two solutions for 1-bit advertisement: shared randomness and pseudorandomness generator.

Enhanced gossip algorithm performance in stable network topologies.

Abstract

In this paper, we study the fundamental problem of gossip in the mobile telephone model: a recently introduced variation of the classical telephone model modified to better describe the local peer-to-peer communication services implemented in many popular smartphone operating systems. In more detail, the mobile telephone model differs from the classical telephone model in three ways: (1) each device can participate in at most one connection per round; (2) the network topology can undergo a parameterized rate of change; and (3) devices can advertise a parameterized number of bits about their state to their neighbors in each round before connection attempts are initiated. We begin by describing and analyzing new randomized gossip algorithms in this model under the harsh assumption of a network topology that can change completely in every round. We prove a significant time complexity gap between the case where nodes can advertise $0$ bits to their neighbors in each round, and the case where nodes can advertise $1$ bit. For the latter assumption, we present two solutions: the first depends on a shared randomness source, while the second eliminates this assumption using a pseudorandomness generator we prove to exist with a novel generalization of a classical result from the study of two-party communication complexity. We then turn our attention to the easier case where the topology graph is stable, and describe and analyze a new gossip algorithm that provides a substantial performance improvement for many parameters. We conclude by studying a relaxed version of gossip in which it is only necessary for nodes to each learn a specified fraction of the messages in the system.