Lower Bounds for Dynamic Distributed Task Allocation

TL;DR

This paper establishes new lower bounds on the minimum number of agent task switches needed in dynamic distributed task allocation, highlighting fundamental limits in multi-agent systems with changing demands.

Contribution

It provides the first non-trivial lower bounds for switching costs in dynamic task allocation, advancing understanding of the problem's inherent complexity.

Findings

Lower bounds of 3 and 4 for switching costs in different parameter ranges.

Switching cost cannot be less than 3 in the studied model.

Fundamental limits on task reallocation efficiency in dynamic settings.

Abstract

We study the problem of distributed task allocation in multi-agent systems. Suppose there is a collection of agents, a collection of tasks, and a demand vector, which specifies the number of agents required to perform each task. The goal of the agents is to cooperatively allocate themselves to the tasks to satisfy the demand vector. We study the dynamic version of the problem where the demand vector changes over time. Here, the goal is to minimize the switching cost, which is the number of agents that change tasks in response to a change in the demand vector. The switching cost is an important metric since changing tasks may incur significant overhead. We study a mathematical formalization of the above problem introduced by Su, Su, Dornhaus, and Lynch, which can be reformulated as a question of finding a low distortion embedding from symmetric difference to Hamming distance. In this model it is trivial to prove that the switching cost is at least 2. We present the first non-trivial lower bounds for the switching cost, by giving lower bounds of 3 and 4 for different ranges of the parameters.