Broadcasting on a budget in the multi-service communication model

G. Itkis, I. Newman, A. Schuster
Proceedings. Fifth International Conference on High Performance Computing (Cat. No. 98EX238)  
which implies the lemma. Let T 0 be an optimal broadcast schedule for for n processors that uses only q k . Certainly heightT heightT 0 . However, heightT 0 = Opolylg n [3, 9] . Proof sketch of Lemma 3.7: The conditions of the Lemma attempt to characterize a schedule T for inputs S; B; n that ends within time H. We first explain the meaning of the conditions in the Lemma. In general, these conditions assert that each level (time point) in the schedule is consistent, based on the consistency of
more » ... revious levels. This fact, together with a consistent starting/ending level, and a total time/budget as required, is enough to assert the existence of the schedule. Now, n t represents the number of new nodes at time t, namely these nodes that correspond to processors that have received the message at time t. These nodes are available to immediately start transmitting the message to other nodes.
doi:10.1109/hipc.1998.737985 dblp:conf/hipc/ItkisNS98 fatcat:d57gzy7yijgbvfj3cl6lusglum