Range Assignment Approximation Based on Steiner Tree in Ad Hoc Wireless Networks

In this paper, we discuss the problem of introducing relay nodes in the given set of original nodes and assigning transmitting ranges to the nodes. The main contribution of this paper is the O(N log N) algorithm to relay nodes to the wireless network and 2-approximation to assign transmitting ranges to nodes (original and relay). The output of the algorithm is the minimal Steiner tree on the graph consists of terminal (original) nodes and relay (additional) nodes. The output of approximation is the range assignments to the nodes.