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Coverage problems related to the wireless sensor networks are widely studied during the last few years. Generally, the coverage of the whole area is taken into account in those studies, giving the entire region the same importance. On the other hand, in the real life, some of the covered regions can be more important compared to other parts. In border surveillance applications, some paths are favored by intruders and it is important to keep these areas under constant surveillance. But keeping these points under constant surveillance means more energy consumption for these sensors and shorter lifetime. In order to solve these contradicting objectives, we introduce the minimum power maximum coverage sensor (MPMC) heuristic. Using MPMC, sensors adjust their ranges and construct clusters during operation to decrease the power consumption with minimum performance loss in coverage and detection. We also present simulation results which indicate the distinctive energy-coverage balance achieved by the proposed heuristic.