Construction of Virtual Backbone on Growth-Bounded Graph with Variable Transmission Range

Virtual backbone has been used extensively in various aspects for wireless ad hoc or sensor networks recently. We propose an approximation solution to construct a virtual backbone based on a more generalized and realistic model of polynomial bounded growth. A localized distributed algorithm of MCDS_GBG for computing a Minimum Connected Dominating Sets as backbone in the growth-bounded graph is presented. This approach consists of three stages: firstly construct an MIS by network decomposition scheme; secondly compute a minimum dominating set in 2-separated collection with r transmission range and finally use Marking process and ruling k to reduce the virtual backbone with 3r transmission range. The computed Connected Dominating Set guarantees a constant stretch factor on the length of a shortest path and induces a subgraph of constant degree while the nodes only require direct neighborhood information. The efficiency of our approach is confirmed through both theoretical analysis and comparison study. Key-Words: Virtual backbone; Growth-bounded graph; Connected dominating sets; Maximal independent sets; Wireless ad hoc sensor network; Network decomposition