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.

中文翻译：

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Ad Hoc无线网络中基于Steiner树的拓扑的范围分配问题

本文介绍了一种在给定的通信图中引入中继节点的有效方法。我们的算法将传输范围分配给节点，以便在图中所有连接的范围分配上，范围分配功能的成本最小。本文的主要贡献是O（N log N）算法，将中继节点添加到无线通信网络中，以及2逼近，以将传输范围分配给节点（原始节点和中继节点）。它不假定通信图为单位磁盘图。该算法的输出是图中的最小Steiner树，该树由终端（原始）节点和中继（其他）节点组成。近似值的输出是对节点的范围分配。