Distributed One-Hope Algorithm based on Steiner Connected Dominating Set in Wireless Networks

Multicast routing problem is to find a tree rooted at a source node to all multicast destination nodes. In dominating set problem, we are required to find a minimum size subset of vertices that each vertex is either in the dominating set or adjacent to some node in the dominating set. In this paper, we concentrate on the related problem of finding a connected dominating set of minimum size in which the graph induced by nodes in the dominating set are required to be connected. Instead of conventional spanning tree model, we used Steiner tree in unit-disk graph to connect nodes. The main contributions of this work are fully distributed Steiner tree with approximation ratio of 2 and fully distributed algorithm for multicast backbone structure with an approximation ratio at most 10. The main advantage of the algorithm is that it simplifies the routing process to one in a smaller subnetwork.