On Distributed Function Computation in Structure-Free Random Networks

TL;DR

This paper analyzes the efficiency of distributed MAX computation in structure-free random wireless networks using Aloha, proposing protocols that approach optimal performance with minimal network structure.

Contribution

It introduces protocols for one-shot and pipelined MAX computation in structure-free networks, achieving near-optimal and scalable performance.

Findings

One-shot MAX computation completes in $O(\sqrt{n/\log n})$ slots.

Pipelined MAX computation achieves rate $\Omega(1/(\log^2 n))$.

Protocols perform close to the best coordinated protocols despite minimal network structure.

Abstract

We consider in-network computation of MAX in a structure-free random multihop wireless network. Nodes do not know their relative or absolute locations and use the Aloha MAC protocol. For one-shot computation, we describe a protocol in which the MAX value becomes available at the origin in $O(\sqrt{n/\log n})$ slots with high probability. This is within a constant factor of that required by the best coordinated protocol. A minimal structure (knowledge of hop-distance from the sink) is imposed on the network and with this structure, we describe a protocol for pipelined computation of MAX that achieves a rate of $\Omega(1/(\log^2 n)).$