We propose the minimum Wiener index spanning tree (MWST) as a routing topology that is suitable for sensor networks with multiple mobile base nodes. However, it was proved that finding a spanning tree with the minimum Wiener index from a weighted graph is NP-hard. To address this problem and analyze the effectiveness of the MWST as the routing tree on sensor networks with multiple mobile base nodes, we designed two algorithms: a branch and bound algorithm for small-scale wireless sensor networks and a simulated annealing algorithm for large-scale wireless sensor networks. The simulation results show that MWST outperforms the minimum spanning tree (MST), one of the representative spanning trees used in many routing protocols for sensor networks, in terms of energy efficiency and packet delay.
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