Abstract. The Quality of Service Multicast Tree Problem is a generalization of the Steiner tree problem which appears in the context of multimedia multicast and network design. In this generalization, each node possesses a rate and the cost of an edge with length l in a Steiner tree T connecting the source to non-zero rate nodes is l 							
						
							
					 															
					Marek Karpinski, Ion I. Mandoiu, Alexander Olshevs