An algorithm for constructing minimal c-broadcast networks

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 [log_c+1(n₁n₂ - i)] = [log_c+1 n₁] + [log_c+1n₂]. Computational results are also provided.