Singing a MIS

TL;DR

This paper introduces the singing model, a broadcast framework where agents emit multiple notes to coordinate in dynamic, asynchronous, and fault-prone networks, achieving fast convergence to a maximal independent set.

Contribution

It presents the first logarithmic-time protocol for MIS in dynamic, network-oblivious settings using the singing model, generalizing the beeping model.

Findings

Converges in O(log n) time with high probability.

Works in asynchronous, dynamic, and fault-prone networks.

First to achieve logarithmic MIS convergence in such settings.

Abstract

We introduce a broadcast model called the singing model, where agents are oblivious of the size and structure of the communication network, even their immediate neighborhood. Agents can sing multiple notes which are heard by their neighbors. The model is a generalization of the beeping model, where agents can only emit sound at a single frequency. We give a simple and natural protocol where agents compete with their neighbors and their strength is reflected in the number of notes they sing. It converges in $O(log(n))$ time with high probability, where $n$ is the number of agents in the network. The protocol works in an asynchronous model where rounds vary in length and have different start times. It works with completely dynamic networks where agents can be faulty. The protocol is the first to converge to an MIS in logarithmic time for dynamic networks in a network oblivious model.