An algorithm for constructing minimal c‐broadcast networks
Shiwoo Lee, José A. Ventura · Networks · 2001
Abstract c‐Broadcasting is a special process to disseminate a single message, originated at any node in a network, to all other nodes of the network by letting each informed node transmit the message to at most c neighbors simultaneously. A minimal c‐broadcast network (c‐mbn) is a communication network in which c‐broadcasting can be completed in minimum time from any node. An optimal c‐broadcast network (c‐obn) is a c‐mbn with the smallest number of edges. Previous studies showed that c‐obn's are extremely difficult to find. A network compounding algorithm is proposed to construct sparse c‐mbn's with n1n2 − i nodes by connecting a subset of nodes from several copies of a c‐mbn with n1 nodes using the structure of another c‐mbn with n2 nodes, such that n1 ≥ 1 and 0 ≤ i < n2, satisfying ⌈logc+1(n1n2 − i)⌉ = ⌈logc+1 n1⌉ + ⌈logc+1n2⌉. Computational results are also provided. © 2001 John Wiley & Sons, Inc.