A 5+ϵ-approximation algorithm for minimum weighted dominating set in unit disk graph

AbstractWe study the minimum weight dominating set problem in weighted unit disk graph, and give a polynomial time algorithm with approximation ratio 5+ϵ, improving the previous best result of 6+ϵ in [Yaochun Huang, Xiaofeng Gao, Zhao Zhang, Weili Wu, A better constant-factor approximation for weighted dominating set in unit disk graph, J. Comb. Optim. (ISSN: 1382-6905) (2008) 1573–2886. (Print) (Online)]. Combining the common technique used in the above mentioned reference, we can compute a minimum weight connected dominating set with approximation ratio 9+ϵ, beating the previous best result of 10+ϵ in the same work

Approximation Algorithmic Performance for CEDS in Wireless Network

A well-organized design of routing protocols in wireless networks, the connected dominating set (CDS) is widely used as a virtual backbone. To construct the CDS with its size as minimum, many heuristic, meta-heuristic, greedy, approximation and distributed algorithmic approaches have been anticipated. These approaches are concentrated on deriving independent set and then constructing the CDS using UDG, Steiner tree and these algorithms perform well only for the graphs having smaller number of nodes. For the networks that are generated in a fixed simulation area. This paper provides a novel approach for constructing the CDS, based on the concept of total edge dominating set. Since the total dominating set is the best lower bound for the CDS, the proposed approach reduces the computational complexity to construct the CDS through the number of iterations. The conducted simulation reveals that the proposed approach finds better solution than the recently developed approaches when important factors of network such as transmission radio range and area of network density varies

Wireless coverage with disparate ranges

Coverage has been one of the most fundamental yet chal-lenging issues in wireless networks. Given a set of nodes and a set of disks of disparate radii, the problem Minimum Disk Cover seeks a disk cover of all nodes with minimum cardi-nality. We present the first polynomial time approximation scheme. We also consider a classical generalization where each input disk is associated with a positive cost, the prob-lem Min-Cost Disk Cover seeks a disk cover of all nodes with minimum total cost. We present a randomized algo-rithm that can achieve an approximation ratio of 2O(log ∗ n) with high probability, where n is the number of input disks. Another line of this work is exploring the relations be-tween disk cover and an important practical problem which seeks a wireless covering schedule of maximum life sub-ject to an energy budget function. We present two algo-rithms: Ellipsoid Algorithm (EA) and Price-Directive Al-gorithm (PDA), and prove that by applying our algorithmic results on disk cover, the approximation ratios for EA and PDA are 2O(log ∗ n) and (1 + ǫ) 2O(log ∗ n) respectively