Optimal deterministic broadcasting in known topology radio networks
We consider deterministic broadcasting in radio networks whose nodes have full topological information about the network. The aim is to design a polynomial algorithm, which, given a graph G with source s, produces a fast broadcast scheme in the radio network represented by G. The problem of finding a fastest broadcast scheme for a given graph is NP-hard, hence it is only possible to get an approximation algorithm. We give a deterministic polynomial algorithm which produces a broadcast scheme of length O(D + log(2) n), for every n-node graph of diameter D, thus improving a result of Gasieniec et al. (PODC 2005) [ 17] and solving a problem stated there. Unless the inclusion NP subset of BPTIME(n(O(log log n))) holds, the length O(D + log(2) n) of a polynomially constructible deterministic broadcast scheme is optimal.
broadcast radio network graph deterministic algorithm