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rdquoApplication-level multicast is a promising alternative to IP multicast due to its independence from the IP routing infrastructure and its flexibility in constructing the delivery trees. The existing overlay multicast systems either support a single data source or have high maintenance overhead when multiple sources are allowed. They are inefficient for applications that require any-source multicast with varied host capacities and dynamic membership. This paper proposes ACOM, an any-source capacity-constrained overlay multicast system, consisting of three distributed multicast algorithms on top of a non-DHT overlay network with simple structures (random overlay with a non-DHT ring) that are easy to manage as nodes join and depart. The nodes have different capacities, and they can support different numbers of direct children during a multicast session. No explicit multicast trees are maintained on top of the overlay. The distributed execution of the algorithms naturally defines an implicit, roughly balanced, capacity-constrained multicast tree for each source node. We prove that the system can deliver a multicast message from any source to all nodes in expected O(logc n) hops, which is asymptotically optimal, where c is the average node capacity and n is the number of members in a multicast group.