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Power conservation is a critical issue for ad hoc wireless networks. The main objective of the paper is to find the minimum uniform transmission range of an ad hoc wireless network, where each node uses the same transmission power, while maintaining network connectivity. Three different algorithms, Prim's Minimum Spanning Tree (MST), its extension with Fibonacci heap implementation, and an area-based binary search are developed to solve the problem. Their performance is compared by simulation study together with Kruskal's MST, a known solution proposed by Ramanathan and Rosales-Hain for topology control by transmission power adjustment, and an edge-based binary search used by the same study in order to find the per-node-minimality after Kruskal's algorithm is applied. Our results show that Prim's MST outperforms both Kruskal's MST and the two binary searches. The performance between Prim's MST implemented with binary heap and Fibonacci heap is fairly close, with the Fibonacci implementation slightly outperforming the other.