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This paper describes an efficient method for introducing relay nodes in the given communication graph. Our algorithm assigns transmitting ranges to the nodes such that the cost of range assignment function is minimal over all connecting range assignments in the graph. The main contribution of this paper is the O(N log N) algorithm to add relay nodes to the wireless communication network and 2-approximation to assign transmitting ranges to nodes (original and relay). It does not assume that communication graph to be a unit disk graph. 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.

Range Assignment Problem on the Steiner Tree Based Topology in Ad Hoc Wireless Networks