On the heterogeneous postal delivery model for multicasting

The heterogeneous postal delivery model assumes that each intermediate node in the multicasting tree incurs a constant switching time for each message that is sent. We have proposed a new model where we assume a more generalized switching time at intermediate nodes. In our model, a child node v of a parent u has a switching delay vector, where the ith element of the vector indicates the switching delay incurred by u for sending the message to v after sending the message to i - 1 other children of u. Given a multicast tree and switching delay vectors at each non-root node in the tree, we provide an O(n^5/2) optimal algorithm that will decide the order in which the internal (non-leaf) nodes have to send the multicast message to its children in order to minimize the maximum end-to-end delay due to multicasting. We also show an important lower bound result that optimal multicast switching delay problem is as hard as min-max matching problem on weighted bi- partite graphs and hence O(n^5/2) running time is tight.