Minimizing interference of a wireless ad-hoc network in a plane

We consider interference minimization in wireless ad-hoc networks. This is formulated as assigning a suitable transmission radius to each of the given points in the plane, so as to minimize the maximum number of transmission ranges overlapping any point. Using ideas from computational geometry and ε{lunate}-net theory, we attain an O (sqrt(Δ)) bound for the maximum interference where Δ is the interference of a uniform-radius ad-hoc network. This generalizes a result given in [P. von Rickenbach, S. Schmid, R. Wattenhofer, A. Zollinger, A robust interference model for wireless ad-hoc networks, in: Proc. 5th International Workshop on Algorithms for Wireless, Mobile, Ad Hoc and Sensor Networks (WMAN), Denver, Colorado, USA, April 2005] for the special case of highway model (i.e., one-dimensional problem) to the two-dimensional case. We show how a distributed algorithm can achieve a slightly weaker bound. We also give a method based on quad-tree decomposition and bucketing that has another provable interference bound in terms of the ratio of the minimum distance to the radius of a uniform-radius ad-hoc network.