Sensor database is a type of database management system which offers sensor data and stored data in its data model and query languages. In this system, when a user poses a query to this sensor database, the query will be disseminated across the database. During this process, each sensor generates data that match the query from its covered area and then returns the data to the original sensor. In order to achieve an energy-efficient implementation, it will be useful to select a minimally sufficient subset of sensors to keep active at any given time. Thus, how to find a subset efficiently is an important problem for sensor database system. We define this problem as sensor database coverage (SDC) problem. In this paper, we reduce the SDC problem to connected set cover problem, then present two approximation algorithms to select a minimum connected set cover for a given sensor database. Moreover, to guarantee robustness and accuracy, we require a fault-tolerant sensor database, which means that each target in a query region will be covered by at least m sensors, and the selected sensors will form a k-connected subgraph. We name this problem as (k,m)-SDC problem and design another approximation algorithm. These three algorithms are the first approximation algorithms with guaranteed approximation ratios to SDC problem. We also provide simulations to evaluate the performance of our algorithms. We compare the results with algorithms in . The comparison proves the efficiency of our approximations. Thus, our algorithms will become a new efficient approach to solve coverage problem in sensor database systems.