— In this paper, we address a sensor network lifetime problem that maintains a certain throughput in an environment where physical node destruction is possible. While lifetime is constrained by limited energy in individual sensors and has been addressed in some detail before, the problem of physical node destruction due to the small form factor and hostile operating conditions of sensors, although significant, has not been addressed before. Specifically, we define a lifetime optimization problem in sensor networks under a representative physical attack model that we define. Our lifetime problem is representative, practical and encompasses other versions of similar problems. Our goal is to derive the minimum number and deployment plan of nodes to meet lifetime requirement. We propose two solutions for this problem. The first solution, PMR, deploys nodes only attempting to minimize energy consumption during routing. We show that this approach may not always be optimal. We then propose ...