Wireless Sensor Networks (WSNs) are subject to node failures because of limited energy and link unreliability which makes the design of routing protocols in such networks a challenging task. The multipath routing scheme is an optimal alternative to address this problem which splits the traffic across multiple paths instead of routing all the traffic along a single path. However, using more paths introduces more contentions which degrade energy efficiency. The problem becomes even more difficult

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... in the scenario of multiple sessions since different source-destination pairs may pass the same link which makes the flow distribution of each link uncertain. Our goal is to minimize the energy cost and provide the robust transmission by choosing the optimal paths. We first study the problem from a theoretical standpoint by mapping it to the multi-commodity network design problem. Since it is hard to build a global addressing scheme due to the great number of sensor nodes, we propose a Distributed Energy Efficient Routing protocol (D2ER). In D2ER, we employ the transportation method which can optimize the flow distribution with minimal energy consumption. Simulation results demonstrate that our optimal algorithm can save energy drastically.