The Range Assignment Problem in Static Ad-Hoc Networks on Metric Spaces

In this paper we study the range assignment problem in static ad-hoc networks on metric spaces. We consider the h-strong connectivity and h-broadcast problems on trees, high dimensional Euclidean spaces and general finite metric spaces. Both homogeneous and nonhomogeneous cases are explored. We show that the h-broadcast problem is polynomial solvable on trees and present an O(n2 )-approximation algorithm for the h-strong connectivity problem on trees, where n is the number of stations. Furthermore, we propose a probabilistic O(log n log log n)approximation algorithm for the h-broadcast problem and a probabilistic O(n2 log n log log n)-approximation algorithm for the h-strong connectivity problem on high dimensional Euclidean spaces and general metric spaces. In the case of high dimensional real normed spaces, if the distance-power gradient 1+ O(log log log n/ log log n), an O(log n)approximation algorithm and an O(n2 log n)-approximation algorithm are developed for the h-broadcast pr...

• Type: Conference
• Year: 2004
• Where: SIROCCO
• Authors: Deshi Ye, Hu Zhang
• Keywords: H-broadcast Problem, H-strong Connectivity Problem, Metric Spaces, SIROCCO 2004, SIROCCO 2007