We study the minimum connected sensor cover problem ($\mathsf{MIN}$-$\mathsf{CSC}$) and the budgeted connected sensor cover ($\mathsf{Budgeted}$-$\mathsf{CSC}$) problem, both motivated by important applications (e.g., reduce the communication cost among sensors) in wireless sensor networks. In both problems, we are given a set of sensors and a set of target points in the Euclidean plane. In $\mathsf{MIN}$-$\mathsf{CSC}$, our goal is to find a set of sensors of minimum cardinality, such that all target points are covered, and all sensors can communicate with each other (i.e., the communication graph is connected). We obtain a constant factor approximation algorithm, assuming that the ratio between the sensor radius and communication radius is bounded. In $\mathsf{Budgeted}$-$\mathsf{CSC}$ problem, our goal is to choose a set of B sensors, such that the number of targets covered by the chosen sensors is maximized and the communication graph is connected. We also obtain a constant approximation under the same assumption.

我们研究了最小连接传感器盖问题（$\mathsf{最小}$--$\mathsf{CSC}$）和预算的已连接传感器盖（$\mathsf{已预算}$--$\mathsf{CSC}$）问题，两者都是由无线传感器网络中的重要应用（例如，减少传感器之间的通信成本）引起的。在这两个问题中，我们都得到了欧几里得平面中的一组传感器和一组目标点。在$\mathsf{最小}$--$\mathsf{CSC}$，我们的目标是找到一组具有最小基数的传感器，以便覆盖所有目标点，并且所有传感器都可以彼此通信（即，已连接通信图）。假设传感器半径和通信半径之比是有界的，我们将获得一个常数因子近似算法。在$\mathsf{已预算}$--$\mathsf{CSC}$问题是，我们的目标是选择一组B传感器，以使所选传感器覆盖的目标数量最大化，并连接通信图。在相同的假设下，我们还获得了一个恒定的近似值。