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 = {s(0), s(1), ... ,s(n)) of radio stations are pre-placed in R-2, and a source station so (say) is marked. In our first problem. the objective is to find a real number r such that 2-hop homogeneous broadcast from so 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 so, provided such an assignment is possible. The first problem is solved in O(n(2.376) logn) time and O(n(2)) space. For the second problem, a 2-factor approximation algorithm is proposed that runs in O(n(2)) time and O(n) space. (C) 2009 Elsevier B.V. All rights reserved.