Polylogarithmic Inapproximability of the Radio Broadcast Problem

We prove that there exists a universal constant c > 0 such that the Radio Broadcast problem admits no additivec · log2 n-approximation, unless NP ⊆ BPTIME(n O(loglog n)). For graphs of at most logarithmic radius, an O(log2 n) additive approximation algorithm is known, hence our lower bound is tight. To the best of our knowledge, this is the first tight additive polylogarithmic approximation result.

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