Studies on neighbourhood graphs for communication in multi agent systems

Authors:
Andreas Goebels
Affiliations:
International Graduate School of Dynamic Intelligent Systems, Knowledge Based Systems, University of Paderborn, Germany
Venue:
ICNC'06 Proceedings of the Second international conference on Advances in Natural Computation - Volume Part II
Year:
2006

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Abstract

This paper addresses a special type of graph, the k-neighbourhood graph, for the usage in huge multi agent systems. It can be used to establish slim communication structures in extensive groups of agents as they are present e.g. in swarm applications. We will prove some properties of k-neighbourhood graphs in two- and three-dimensional Euclidean space, i.e. we show that the maximum number of incoming connections per agent is limited to a value independent from the overall number of agents in the system. For the two-dimensional case we prove a maximum in-degree of 6 ·k. Furthermore, for agents interacting in three dimensions an upper and a lower bound for this value is presented.