No Time to Interact: Simulating Population Protocols at Scale

Abstract

We consider the simulation of population protocols with a random scheduler. A population protocol consists of n agents each associated a state q_i ∈ Q where |Q| = 𝒪(log n) for many protocols. An execution consists of a large number I ≫ n of interactions, each time selecting two agents uniformly at random and updating their state solely based on the current states of the pair.
We propose - to the best of our knowledge - a novel and faithful simulation technique: we show that a protocol’s (undirected) interaction multi-graph follows the configuration model with a Poisson degree distribution (up to some rejection). We then introduce a sampling algorithm for the component structure of the configuration model which we believe to be of independent interest. In the subcritical regime, its runtime scales in the number of component types rather than the graph size. Finally, we show how to accelerate the simulation of a protocol by using the component structure as an execution plan template. For any fixed integer parameter τ ≥ 2 and I ≫ n, the time taken per n interactions is in 𝒪(|Q|^{2-2/τ} n^{1/τ}) (where the hidden constant depends heavily on τ).
In an experimental evaluation, we give evidence to the practicality of our approach. For large systems, we observe a speedup of several orders of magnitude over state-of-the-art simulators.