A Distributed Augmenting Path Approach for the Bottleneck Assignment Problem

TL;DR

This paper introduces a distributed algorithm for the Bottleneck Assignment Problem, focusing on how to efficiently search for augmenting paths across a network of agents, and compares two methods for this search.

Contribution

It presents a novel distributed approach to solve BAP, particularly addressing the challenge of augmenting path search and formalizing subset solution conditions.

Findings

Two methods for augmenting path search are compared.

The proposed approaches are validated through numerical analysis.

The distributed algorithm effectively solves BAP in networked environments.

Abstract

We develop an algorithm to solve the Bottleneck Assignment Problem (BAP) that is amenable to having computation distributed over a network of agents. This consists of exploring how each component of the algorithm can be distributed, with a focus on one component in particular, i.e., the function to search for an augmenting path. An augmenting path is a common tool used in most BAP algorithms and poses a particular challenge for this distributed approach. Given this significance, we compare two different methods to search for an augmenting path in a bipartite graph. We also exploit properties of the augmenting paths to formalise conditions for which the solution from subsets of the sets of agents and tasks can be used to solve the BAP with the full sets of agents and tasks. In the end, we evaluate and compare the derived approaches with a numerical analysis.