Modelling gateway placement in wireless networks: geometric k-centres of unit disc graphs

Authors:
Stephane Durocher;Krishnam Raju Jampani;Anna Lubiw;Lata Narayanan
Affiliations:
University of Waterloo, Waterloo, ON, Canada;University of Waterloo, Waterloo, ON, Canada;University of Waterloo, Waterloo, ON, Canada;Concordia University, Montreal, PQ, Canada
Venue:
Proceedings of the fifth international workshop on Foundations of mobile computing
Year:
2008

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Abstract

Motivated by the gateway placement problem in wireless networks, we consider the geometric k-centre problem on unit disc graphs: given a set of points P in the plane, find a set F of k points in the plane that minimizes the maximum graph distance from any vertex in P to the nearest vertex in F in the unit disc graph induced by P union F. We describe exact and approximate polynomial-time solutions to this problem for any fixed k and show that the problem is NP-hard when k is an arbitrary input parameter.