Broadcasting is an information dissemination process in communication networks whereby a message, originated at any node of a network, is transmitted to all other nodes of the network. In c-broadcasting, each node having the message completes up to c transmissions to its neighbors over the communication lines in one time unit. In a k-fault tolerant c-broadcast network, the broadcasting process can be accomplished even if k communication lines fail. This paper presents innovative binary linear programming formulations to construct c-broadcast graphs, k-fault-tolerant c-broadcast graphs, and their time-relaxed versions. The proposed mathematical models are used to generate eight previously unknown minimum c-broadcast graphs, new upper bounds for eleven other instances of the c-broadcast problem, and over 30 minimum k-fault-tolerant c-broadcast graphs. The paper also provides a construction method to produce an upper bound for an infinite family of k-fault-tolerant c-broadcast graphs.
All Science Journal Classification (ASJC) codes
- Discrete Mathematics and Combinatorics
- Applied Mathematics