Discrete consensus for asynchronous distributed task assignment

This paper deals with the problem of assigning tasks to a set of nodes communicating in a connected graph topology to satisfy the following requirements: assigning all the tasks to the agents; assigning to each agent no more than M tasks; minimizing the maximum total load of each agent. A gossip-based algorithm is presented: starting from an unfeasible solution, at each iteration a node solves a Local-Integer Linear Programming problem with its neighbors (i.e., the connected nodes in the communication graph). The convergence of the algorithm is proved and the expected convergence time is evaluated. A simulation campaign shows experimental results on the performance of the proposed approach.