Maximum coverage of radius-one sources in the wireless communication

In this article we study a coverage problem in wireless communication called Maximum Points Coverage Problem. Given m sources on a two-dimensional grid and each source covers a circular area that has a radius of one, the problem is to determine the maximum number of grid points that can be covered by the m sources while all the m sources must maintain communication among themselves. We show that m sources of radius one can cover 3m+2 points and that the exact upper bound of the grid points that can be covered by m sources currently in range is the same number as 3m + 2. Additionally, we also give an algorithm to place these 3m+2 sources on a two-dimensional grid. Future research is discussed and a list of open problems is given in the conclusion.