Multiagent Matching Algorithms with and without Coach

A matching is a (one-to-one) mapping between two sets, satisfying some given constraints. In a multiagent scenario, i.e. in a setting where at least one of the sets corresponds to a group of agents, a number of interesting facets are added to this general matching problem. Therefore, in this paper, we discuss several different matching criteria, where preference between elements is based on their distance (not on rankings), and state their relationship to well-known criteria, e.g. Pareto efficiency. We also introduce algorithms for computing matchings. The first one (LocalMatch), a decentralized algorithm, requires only communication between pairs of agents. The second algorithm (GlobalMatch) with a central control agent, called coach, computes a globally maximal matching, i.e., where the maximal distance in the matching is minimized not only for the whole set of elements, but also for each submatching, in O(n logn) time. Especially this kind of matching has applications in multiagent systems for solving transportation problems, coordination of rescue robots, and marking in (simulated) robotic soccer, which is addressed in this paper.