A coordination-free distributed algorithm for simple assignment problems using randomized actions

In this paper, we present a distributed algorithm for simple assignment problems in multi-agent systems without the presence of a central or a local coordinator. In a simple assignment problem, a unique task is to be assigned to each agent assuming that the cost of each assignment is identical. We assume that the communication among the agents is restricted over a sparse network, i.e., no agent can communicate to all of the other agents in the network. We propose a coordination-free, memoryless, distributed algorithm that is based on inter-agent information exchange via a gossip (type) communication protocol. Each agent randomly picks a task and then either swaps its task with a randomly chosen neighbor from its neighborhood (if they have different tasks) or one of them randomly picks a new task (if they have the same task). We first consider the case when the agents have no memory such that they do not have information regarding their task and neighbor history. We then present a modification when the agents possess memory. Finally, we show that both schemes converge to the set of acceptable configurations.