Uncertainty Intervals for Robust Bottleneck Assignment

TL;DR

This paper develops algorithms to compute uncertainty bounds for bottleneck assignment problems, ensuring robustness against weight perturbations, and demonstrates their effectiveness through a multi-agent task assignment example.

Contribution

It introduces two novel algorithms for deriving uncertainty bounds in bottleneck assignment problems, guaranteeing invariance within these bounds.

Findings

Algorithms provide tight uncertainty bounds

Bottleneck assignment remains invariant within bounds

Effective application demonstrated in multi-agent task assignment

Abstract

We examine the robustness of bottleneck assignment problems to perturbations in the assignment weights. We derive two algorithms that provide uncertainty bounds for robust assignment. We prove that the bottleneck assignment is guaranteed to be invariant to perturbations which lie within the provided bounds. We apply the method to an example of task assignment for a multi-agent system.