Algorithmic Aspects for Independent and Dominating Sets in Mobile Ad Hoc Networks

Clustering in mobile ad hoc networks (MANETs) is an important method to management and routing in such networks. Once the clusters are created, the manger (coordinators) of the clusters may be used to form a backbone for efficient routing and communication purposes. A set of clusters may also provide the underlying physical structure for multicast communication for a higher level group communication module which may effectively be used for fault tolerance and key management for security purposes. Graph representing method for clustering in MANETs and show that although there is a wide range of such algorithms. MANEts are advancing rapidly, both in research and more and more into our everyday lives. MANETs are a prime example of a new technology that has gained a lot of attention in the literature, and that is going to enhance the way we view and interact with the environment. These mobile ad hoc networks are modeled by communication graphs which give the communication links between some devices or nodes equipped with wireless transceivers or radios. Independent and dominating sets are prominently used in the efficient organization of large-scale MANETs. In a communication graph, an independent set consists of vertices that cannot communicate with one another directly. Such a set is commonly used in clustering strategies, e.g. to obtain a hierarchical view of the network. The algorithmic complexity clustering is known to be NP-Complete for simple undirected graphs. For the special family of graphs that represent MANETs, modeled as unit disk graphs, we introduce a two phase distributed polynomial time and message complexity approximation solution with O(k) worst case ratio over the optimal solution. The first phase constructs a spanning tree of the network and the second phase then partitions the spanning tree into sub trees with bounded diameters.