Power Assignment for k-Connectivity in Wireless Ad Hoc Networks

The problem Min-Power k-Connectivity seeks a power assignment to the nodes in a given wireless ad hoc network such that the produced network topology is k-connected and the total power is the lowest. In this paper, we present several approximation algorithms for this problem. Specifically, we propose a 3k-approximation algorithm for any k ≥ 3, a (k + 12H (k)) -approximation algorithm for k(2k-1) ≤ n where n is the network size, a (k + 2⌈(k + 1)/2⌉)-approximation algorithm for 2 ≤ k ≤ 7, a 6-approximation algorithm for k = 3, and a 9-approximation algorithm for k = 4.