Homogeneous 2-hop broadcast in 2D

In this paper, two variations of the minimum cost homogeneous range assignment problem for 2-hop broadcast from a given source are considered. A set S={s0,s1,…,sn} of radio stations are pre-placed in R2, and a source station s0 (say) is marked. In our first problem, the objective is to find a real number r such that 2-hop homogeneous broadcast from s0 is possible with range r, and the total power consumption of the entire network is minimum. In the second problem, a real number r is given and the objective is to identify the smallest subset of S for which range r can be assigned to accomplish the 2-hop broadcast from s0, provided such an assignment is possible. The first problem is solved in O(n2.376logn) time and O(n2) space. For the second problem, a 2-factor approximation algorithm is proposed that runs in O(n2) time and O(n) space.