Interference Reduction in Directional Wireless Networks

Abstract

In a wireless network using directional transmitters, a typical problem is to schedule a set of directional links to cover all the receivers in a region, such that an adequate data rate and coverage are maintained while minimizing interference. We can model the coverage area of a directional transmitter as an unit triangle and the receiver as a point in the plane. Motivated by this, we first consider a minimum ply covering (MPC) problem. We propose a 2-approximation algorithm for the MPC problem in $O((opt+n)m^{14opt+1}(\log opt))$ time, where m is the number of transmitters and n is the number of receivers given in the plane, and $opt$ is the maximum number of triangles, in the optimal solution, covering a point in the plane. We also show that the MPC problem is NP-hard, and is not $(2-\epsilon )$-approximable for any $\epsilon >0$ unless P = NP. We also study channel allocation in directional wireless networks by posing it as a colorable covering problem, namely, 3-colorable unit triangle cover (3CUTC). We propose a simple 4-approximation algorithm in $O(m^{30}n^2)$ time, for this problem.