Proof of optimal algorithm for maximum-bandwidth ALM tree construction

We construct an ALM (application layer multicast) tree that achieves the maximum bandwidth by using underlay traffic information. Since this problem was previously shown to be NP-hard, no polynomial-time algorithms for maximum-bandwidth ALM tree construction exist. In our work, we assume that the underlay network has a tree network topology, and we show a polynomial-time algorithm that constructs a maximum-bandwidth ALM tree on such a tree network topology. We propose an ALM tree construction algorithm that achieves bandwidth b and apply this algorithm with various bandwidth values b. We show that it can make a maximum-bandwidth ALM tree in polynomial time.