Homogeneous 2-hop broadcast in 2D

Authors:
Gautam K. Das;Sandip Das;Subhas C. Nandy
Affiliations:
University of New Brunswick, Fredericton, Canada -- E3B 5A3;Indian Statistical Institute, Kolkata -- 700 108, India;Indian Statistical Institute, Kolkata -- 700 108, India
Venue:
Computational Geometry: Theory and Applications
Year:
2010

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Abstract

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 s"0 (say) is marked. In our first problem, the objective is to find a real number r such that 2-hop homogeneous broadcast from s"0 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 s"0, provided such an assignment is possible. The first problem is solved in O(n^2^.^3^7^6logn) 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.