—We investigate the p-percent coverage problem in this paper and propose two algorithms to prolong network lifetime based on the fact that for some applications full coverage is not necessary and different subareas of the monitored area may have different coverage requirements. The first algorithm, CPCA, is a centralized algorithm which selects the least number of nodes to monitor p-percent of the monitored area. The second algorithm, DPCP, is a distributed algorithm which can determine a set of nodes in a distributed manner to cover p-percent of the monitored area. Both of the algorithms guarantee network connectivity. The simulation results show that our algorithms can remarkably prolong network lifetime, have less than 5% unrequired coverage for large networks and employ nodes fairly for most cases.