An Upper and Lower Bound for the Convergence Time of House-Hunting in Temnothorax Ant Colonies

Abstract

We study the problem of house-hunting in ant colonies, where ants reach consensus on a new nest and relocate their colony to that nest, from a distributed computing perspective. We propose a house-hunting algorithm that is biologically inspired by Temnothorax ants. Each ant is modeled as a probabilistic agent with limited power, and there is no central control governing the ants. We show an $\Omega \left(logn\right)$ lower bound on the running time of our proposed house-hunting algorithm, where n is the number of ants. Furthermore, we show a matching upper bound of expected $O\left(logn\right)$ rounds for environments with only one candidate nest for the ants to move to. Our work provides insights into the house-hunting process, giving a perspective on how environmental factors such as nest quality or a quorum rule can affect the emigration process.