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 $$\mathcal{O}(D + \log ^2 n)$$, for every n-node graph of diameter D, thus improving a result of Gąsieniec et al. (PODC 2005) [17] and solving a problem stated there. Unless the inclusion NP $$\subseteq$$ BPTIME($$n^{\mathcal{O}(\log \log n)})$$ holds, the length $$\mathcal{O}(D + \log ^2 n)$$ of a polynomially constructible deterministic broadcast scheme is optimal.

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