Energy efficient multicast routing in ad hoc wireless networks with discrete levels of transmission power

In this paper, we discuss the energy efficient multicast problem in ad hoc wireless networks. We assume that each node in the network has a set of discrete levels of transmission power and nodes are relatively static. The problem is, given a set of nodes in the Euclidean plane and a multicast request, to construct a multicast tree rooted at the source and including all destinations such that the total energy cost of the transmitting nodes in the tree is minimized. We first prove that this problem is NP-hard and is unlikely to have an approximation algorithm with a logarithmic performance ratio. We then propose two algorithms, one is based on the Steiner tree method and the other is based on connected dominating set method. Both algorithms have guaranteed performance ratios and outperform the existing method.