Centralized asynchronous broadcast in radio networks

We study asynchronous broadcasting in packet radio networks. A radio network is represented by a directed graph, in which one distinguished source node stores a message that needs to be disseminated among all the remaining nodes. An asynchronous execution of a protocol is a sequence of events, each consisting of simultaneous deliveries of messages. The correctness of protocols is considered for specific adversarial models defined by restrictions on events the adversary may schedule. A protocol specifies how many times the source message is to be retransmitted by each node. The total number of transmissions over all the nodes is called the work of the broadcast protocol; it is used as complexity measure. We study computational problems, to be solved by deterministic centralized algorithms, either to find a broadcast protocol or to verify the correctness of a protocol, for a given network. The amount of work necessary to make a protocol correct may have to be exponential in the size of network. There is a polynomial-time algorithm to find a broadcast protocol for a given network. We show that certain problems about broadcasting protocols for given networks are complete in NP and co-NP complexity classes.