1. Embedding trees * Consider a network of one server and N = 3 peers, given that (1) us = 2, U1 = 3, u2 = 2, and U3 = 1 (all in Mbps), (2) all nodes have unlimited download capacity, and (3) each peer in a multicast tree can upload to any number of peers. (a) Find the maximum multicast rate rmar. Draw a multi-tree that achieves this maximum. (b) Find the rate ri of the ith multicast tree, for all i = 1, ...,T, where T is the number of multicast trees from part (a). (c) Now consider a network with one server and N = 3 peers, with us = 3, U1 = 3, U2 = 2, and uz = 1 (in Mbps). But now we impose the constraint that each peer in a multicast tree can only upload to at most one peer, so as to limit the overhead in maintaining the states of the peers. Draw the resulting multi-tree that achieves the maximum multicast rate, and compute the per-tree rates ri. 1. Embedding trees * Consider a network of one server and N = 3 peers, given that (1) us = 2, U1 = 3, u2 = 2, and U3 = 1 (all in Mbps), (2) all nodes have unlimited download capacity, and (3) each peer in a multicast tree can upload to any number of peers. (a) Find the maximum multicast rate rmar. Draw a multi-tree that achieves this maximum. (b) Find the rate ri of the ith multicast tree, for all i = 1, ...,T, where T is the number of multicast trees from part (a). (c) Now consider a network with one server and N = 3 peers, with us = 3, U1 = 3, U2 = 2, and uz = 1 (in Mbps). But now we impose the constraint that each peer in a multicast tree can only upload to at most one peer, so as to limit the overhead in maintaining the states of the peers. Draw the resulting multi-tree that achieves the maximum multicast rate, and compute the per-tree rates ri