On the convergence of puck clustering systems

Puck clustering involves the physical relocation of small objects known as 'pucks' from random positions to a central location, which need not be specified a priori. The evolution of systems of clusters of pucks under the action of robots capable of moving pucks from several locations is considered. A general set of conditions by which a puck collection system may be seen to evolve to a one-cluster system is developed. General conditions leading to clustering behavior in the presence and absence of non-embodied agents are derived. Conditions leading to more efficient algorithms are also derived. Several examples are given to illustrate both non-embodied and embodied puck clustering systems. (C) 2001 Elsevier Science B.V. All rights reserved.