Distributed Broadcast in Wireless Networks with Unknown Topology

TL;DR

This paper investigates the time complexity of broadcast and multi-broadcast protocols in unknown multi-hop wireless networks, establishing new bounds and protocols that are nearly optimal, especially for networks with small diameter and degree.

Contribution

It introduces new theoretical bounds and nearly optimal distributed protocols for broadcast operations in unknown wireless networks, linking them to combinatorial concepts.

Findings

New lower bounds on broadcast time in unknown networks.

Nearly tight upper bounds that improve exponentially for certain network parameters.

Connections established between broadcast problems and combinatorial set families.

Abstract

A multi-hop synchronous wirelss network is said to be unknown if the nodes have no knowledge of the topology. A basic task in wireless network is that of broadcasting a message (created by a fixed source node) to all nodes of the network. The multi-broadcast that consists in performing a set of r independent broadcasts. In this paper, we study the completion and the termination time of distributed protocols for both the (single) broadcast and the multi-broadcast operations on unknown networks as functions of the number of nodes n, the maximum eccentricity D, the maximum in-degree Delta, and the congestion c of the networks. We establish new connections between these operations and some combinatorial concepts, such as selective families, strongly-selective families (also known as superimposed codes), and pairwise r-different families. Such connections, combined with a set of new lower and upper bounds on the size of the above families, allow us to derive new lower bounds and new distributed protocols for the broadcast and multi-broadcast operations. In particular, our upper bounds are almost tight and improve exponentially over the previous bounds when D and Delta are polylogarithmic in n. Network topologies having ``small'' eccentricity and ``small'' degree (such as bounded-degree expanders) are often used in practice to achieve efficient communication.