Rapid Rumor Ramification: Approximating the minimum broadcast time (Extended Abstract)

Given an undirected graph representing of processors, and a source node containing a network a message that must be broadcast to all the nodes, find a scheme that accomplishes the broadcast in the minimum number of time steps. A t each time step, any processor that has received the message is allowed t o communicate the message to at most one of its neighbors in the network, i.e. can communicate via a telephone call to a neighbor. This has been termed the minimum broadcast time problem under the telephone model and is known to be NP-complete. The minimum broadcasl time an a graph is closely related to the poise of the graph. The poise of a tree i s defined t o be the quantity (maximum degree of any node in the tree + diameter of the tree). The poise of a graph is the minimum poise of any of its spanning trees. Computing the poise of a graph as shown to be NP-hard and an algorilhm for computing a spanning tree of approximately minimum poise is derived. This algorithm is then used to derive an O(&)approximation for the minimum broadcast time problem on an n-node graph. Our algorithm extends to many generalizations of the problem such as the multicast problem, a telephone model allowing conference calls, and t o the closely related minimum gossip time problem. *Most of this work was done while the author was at the De partment of Computer Science, University of California, Davis, and supported by NSF Grant CCR-91-03937. The author also acknowledges support from a DIMACS postdoctoral fellowship. 0272-5428/94 $04.00 Q 1994 IEEE 202