Abstract
A core-based forwarding multicast tree is a shortest path tree rooted at core node that distributes multicast packets to all group members via the tree after the packets are sent to the core. Traditionally, the bandwidth cost consumed by transmitting a packet from the core via the tree is evaluated by the total weights of all the edges. And, the bandwidth cost is minimized by constructing the multicast tree that has minimum total weights of edges to span all group members. However, when the local broadcast operation is used to multicast a packet, we found that the bandwidth cost is supposed to be evaluated by the total weights of all senders that include the core and all non-leaves. Since the multicast tree with the number of nodes greater than or equal to three has minimum bandwidth cost only when the core is not a leaf, it leads us to find the multicast tree with the minimum number of non-leaves when each sender node has a unit weight. However, no polynomial time approximation scheme can be found for the minimum non-leaf multicast tree problem unless P = NP since the problem is not only NP-hard but also MAX-SNP hard. Thus, a heuristic is proposed to dynamically reduce the number of non-leaves in the multicast tree. Experimental results show that the multicast tree after the execution of our method has smaller number of non-leaves than others in the geometrically distributed network model.