Time-optimal parallel algorithms for constructing optimal virtual cellular networks

In a cellular network, the base stations are not necessarily uniformly distributed, and their corresponding cell sizes are not necessarily the same. For example, a cell in a well-populated city cell is usually smaller than a cell in a rural area. To study a cellular network with non-uniform cell sizes, one approach is to use a virtual cellular network with a uniform cell size such that each virtual cell contains at most one base station. This paper has proposed parallel algorithms for meshes with multiple broadcasting to construct virtual mesh and honeycomb cellular networks for non-uniformly distributed base stations. The constructed virtual cellular networks are optimal in the sense that their corresponding uniform cell sizes reach the largest possible. The algorithms run in O(log n) time on a mesh with multiple broadcasting of size n×n to construct optimal virtual mesh and honeycomb cellular networks for n non-uniformly distributed base stations. Furthermore, those algorithms are time-optimal.