Computation in anonymous networks

TL;DR

This paper explores a computational model for networks of simple, memory-limited agents without global information, analyzing their ability to compute functions like plurality and approximate counting.

Contribution

It introduces a new model for anonymous, memory-limited agents and provides tight protocols for computing specific functions within this framework.

Findings

Protocols for plurality with O(log k) memory

Protocols for approximate counting with O(log log n) memory

Characterization of the computational power of the model

Abstract

We identify and investigate a computational model arising in molecular computing, social computing and sensor network. The model is made of of multiple agents who are computationally limited and posses no global information. The agents may represent nodes in a social network, sensors, or molecules in a molecular computer. Assuming that each agent is in one of $k$ states, we say that {\em the system computes} $f:[k]^{n} \to [k]$ if all agents eventually converge to the correct value of $f$. We present number of general results characterizing the computational power of the mode. We further present protocols for computing the plurality function with $O(\log k)$ memory and for approximately counting the number of nodes of a given color with $O(\log \log n)$ memory, where $n$ is the number of agents in the networks. These results are tight.