Minimization of Backbone Nodes in Wireless Mobile Backbone Networks using Approximation Algorithms

Abstract

We study a novel hierarchical wireless networking approach in which some of the nodes are more capable than others. In such networks, the more capable nodes can serve as Mobile Backbone Nodes and provide a
backbone over which end-to-end communication can take place. Our approach consists of controlling the mobility of the Backbone Nodes in order to maintain connectivity. We formulate the problem of minimizing the number of backbone nodes and refer to it as the Connected Disk Cover (CDC) problem. We show that it can be decomposed into the Geometric Disk Cover (GDC) problem and the Steiner Tree Problem with Minimum Number of Steiner Points (STP-MSP). We prove that if these sub problems are solved separately by g- and d– approximation algorithms, the approximation ratio of the joint solution is g+d. Then, we focus on the two sub problems and present a number of distributed approximation algorithms that maintain a solution to the GDC problem under mobility. We show that this approach can be extended in order to obtain a joint approximate solution to the CDC problem.