A Distributed Augmenting Path Approach for the Bottleneck Assignment Problem

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.