Deploying base stations for simple user traces in mobile networks

In practice, mobile networks often contain nodes with higher hierarchy that possess better capabilities. These nodes, often called base stations or routers, act as coordinators of end-to-end communications or as liaisons to other networks. It is a long standing problem to select proper locations for base stations in order to better serve all users in the network. Many researches focused on different criteria to deploy base stations. In this paper, we study the base station deployment problem with mobile user traces by finding a minimum disk cover. Since user traces are often simple, predictable or pre-determined, the moving traces are considered as polylines. We define the minimum geometric disk cover for line segments problem (MGDCL) and prove that the MGDCL problem is NP-hard. We approach the MGDCL problem using two cases; one considers parallel line segments, and the other considers line segments of arbitrary directions. We develop algorithms that produce approximate disk covers in both cases. The algorithms are proven to efficiently produce 4-approximation results. Therefore, a satisfactory base station deployment plan can be constructed. In the future, the algorithms are expected to be extended to a more general case, such as base station deployment in the presence of obstacles or in a terrain, or in 3D space.