Singing a MIS

2025-12-02

AI Summary

This paper addresses the problem of computing a maximal independent set (MIS) efficiently in a fully dynamic, network-oblivious (i.e., nodes have no knowledge of network size or topology), asynchronous distributed system. To this end, we introduce the “singing model”—a novel communication abstraction based on multi-tone broadcasting that enables concurrent contention across multiple frequencies, generalizing and strengthening the classical beeping model. We design a decentralized protocol relying solely on local interactions, integrating asynchronous concurrency control with fault-tolerant state updates. The protocol converges to an MIS with high probability within O(log n) rounds—the first such logarithmic-time result for MIS under fully dynamic, zero-knowledge settings. It exhibits strong robustness against node failures and frequent topology changes, significantly advancing the state of the art in dynamic distributed graph algorithms.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Distributed Search
• Planning, Routing, and Scheduling: Scheduling under Uncertainty

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Large-scale security measurements

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.

Problem

• Designing a network-oblivious MIS protocol for dynamic networks
• Enabling agents to compete via multi-note singing communication
• Achieving logarithmic convergence in asynchronous, faulty environments

Innovation

• Generalized beeping model with multiple notes
• Competitive protocol based on singing strength
• Logarithmic convergence in dynamic asynchronous networks