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Energy minimization is a central issue for wireless sensor networks (WSNs). We propose an energy minimization model and suggest a solution algorithm for multi-hop flat routing for WSN. This model is based on some directed minimum spanning trees and the related tree packing problem. We compare this model and some known optimization model and algorithms for two-hop hierarchical routings. In our computational experiments, the model for the flat routing has smaller energy consumption and longer lifetime than those for hierarchical routing. We also show that the weakness of the lifetime of hierarchical routing can be cured by giving extra energy for some super sensors that can be candidates of the heads of the clusters of the hierarchical routing.