Information Gathering in Ad-Hoc Radio Networks with Tree Topology

TL;DR

This paper investigates efficient deterministic and randomized protocols for collecting rumors in ad-hoc tree-structured radio networks without collision detection, achieving optimal or near-optimal times with various message constraints.

Contribution

It introduces new deterministic and randomized algorithms for rumor gathering in ad-hoc trees, including optimal bounds for unbounded and bounded message models.

Findings

Deterministic O(n)-time protocol with unbounded messages

Deterministic O(n log n)-time protocol with bounded messages

Randomized O(n log n)-time protocol for unlabeled nodes

Abstract

We study the problem of information gathering in ad-hoc radio networks without collision detection, focussing on the case when the network forms a tree, with edges directed towards the root. Initially, each node has a piece of information that we refer to as a rumor. Our goal is to design protocols that deliver all rumors to the root of the tree as quickly as possible. The protocol must complete this task within its allotted time even though the actual tree topology is unknown when the computation starts. In the deterministic case, assuming that the nodes are labeled with small integers, we give an O(n)-time protocol that uses unbounded messages, and an O(n log n)-time protocol using bounded messages, where any message can include only one rumor. We also consider fire-and-forward protocols, in which a node can only transmit its own rumor or the rumor received in the previous step. We give a deterministic fire-and- forward protocol with running time O(n^1.5), and we show that it is asymptotically optimal. We then study randomized algorithms where the nodes are not labelled. In this model, we give an O(n log n)-time protocol and we prove that this bound is asymptotically optimal.