Idle Ants Have a Role

TL;DR

This paper presents a distributed algorithm inspired by ant colonies to explain the high number of idle ants and the low survival rate of new colonies, showing that idle ants significantly improve task completion efficiency.

Contribution

It extends a biological task allocation model with a new distributed algorithm demonstrating the critical role of idle ants in colony efficiency.

Findings

Idle ants enable faster task completion with an $O( ext{ln} n)$ bound.

Without idle ants, task completion time is at least linear, $ ext{Ω}(n)$.

The model explains the low survivability of new colonies due to lack of idle ants.

Abstract

Using elementary distributed computing techniques we suggest an explanation for two unexplained phenomena in regards to ant colonies, (a) a substantial amount of ants in an ant colony are idle, and (b) the observed low survivability of new ant colonies in nature. Ant colonies employ task allocation, in which ants progress from one task to the other, to meet changing demands introduced by the environment. Extending the biological task allocation model given in [Pacala, Gordon and Godfray 1996] we present a distributed algorithm which mimics the mechanism ants use to solve task allocation efficiently in nature. Analyzing the time complexity of the algorithm reveals an exponential gap on the time it takes an ant colony to satisfy a certain work demand with and without idle ants. We provide an $O(\ln n)$ upper bound when a constant fraction of the colony are idle ants, and a contrasting lower bound of $\Omega(n)$ when there are no idle ants, where $n$ is the total number of ants in the colony.