2.1. Terminology

We assume a fixed network topology with N nodes where V and D represent the set of all nodes and the set of destination nodes in the multicast application, respectively. Without loss of generality, node 1 is the source node, and it sends a message to all nodes in the set D ? V. Each node may receive the multicast message either directly from the source or over a relay node that is retransmitting the message. Any node may transmit the message at most once, and such nodes are called hop nodes, including the source node. Note that several hop nodes may transmit simultaneously. Leaf nodes receive the message, but do not retransmit it. The number of hops from node 1 to node i is defined as the delay of node i. Our objective is to construct a multicast tree with minimum total power consumption such that no delay bound constraint is violated.

The power required to transmit a message from node i to node j in the network is proportional to where d _ij is the Euclidean distance between nodes i, j, and ? is a constant that depends on the channel medium. In general, ? is assumed to be between 2 and 4. Note that the locations of the nodes are fixed and known, and we let P be an N N