In wireless mesh networks such as WLAN (IEEE 802.11s) or WMAN (IEEE 802.11), each node should help to relay packets of neighboring nodes toward gateway using multi-hop routing mechanisms. Wireless mesh networks usually intensively deploy mesh nodes to deal with the problem of dead spot communication. However, the higher density of nodes deployed, the higher radio interference occurred. This causes significant degradation of system performance. In this paper, we first convert network problems into geometry problems in graph theory, and then solve the interference problem by geometric algorithms. We first define line intersection in a graph to reflect radio interference problem in a wireless mesh network. We then use plan sweep algorithm to find intersection lines, if any; employ Voronoi diagram algorithm to delimit the regions among nodes; use Delaunay Triangulation algorithm to reconstruct the graph in order to minimize the interference among nodes. Finally, we use standard deviation to prune off those longer links (higher interference links) to have a further enhancement. The proposed hybrid solution is proved to be able to significantly reduce interference in a wireless mesh network in O(n log n) time complexity.
International Journal on Applications of Graph Theory in Wireless Ad Hoc Networks and Sensor Networks , vol. abs/1003.3, no. 1, pp. 62-85