On the Reconstruction of a Quality Virtual Backbone in a Wireless Sensor Network With Faulty Links
Jiarong Liang, Feng He, Dajin Wang, Qingnian Li
Abstract
The work of routing and topological control for a wireless sensor network (WSN) is often undertaken by means of its virtual backbone (VB). Usually, a WSN and its VB can be modeled as a unit disk graph (UDG) and a corresponding connected dominating set (CDS), respectively. A smaller CDS in a UDG is preferred because it will lead to less overhead. In practical applications, sensor nodes or their links in a WSN may fail due to obstacles or accidental damage. Thus, it is desirable to either construct a robust VB or be able to reconstruct a new VB. In this article, the problem of reconstructing CDSs for UDGs with faulty links is considered. First, we propose a centralized approximation algorithm for the problem. We theoretically show that for a given UDG, the size of the CDS constructed by our algorithm does not exceed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\xi \cdot opt+\gamma +2m$</tex-math></inline-formula> , where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\xi \cdot opt+\gamma$</tex-math></inline-formula> is the upper bound on the original CDS size, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$opt$</tex-math></inline-formula> is the minimum CDS size in the UDG, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\xi$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\gamma$</tex-math></inline-formula> are two positive constants, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$m$</tex-math></inline-formula> is the number of faulty links. Next, we design a distributed approximation algorithm on the basis of our centralized approximation algorithm and analyze its time and message complexity. Related simulation experiments are presented to compare our algorithm with other state-of-the-art algorithms for solving this problem, and the results show that our algorithm outperforms its competitors.