Polylogarithmic Additive Inapproximability of the Radio Broadcast Problem
Michael Elkin, Guy Kortsarz · SIAM Journal on Discrete Mathematics · 2005
The input for the radio broadcast problem is an undirected n-vertex graph G and a source node s. The goal is to send a message from s to the rest of the vertices in the minimum number of rounds. In a round, a vertex receives the message only if exactly one of its neighbors transmits. The radio broadcast problem admits an $O(\log^2 n)$ approximation [CW-87,KP-04]. [I. Chlamtac and O. Weinstein, in Proceedings of the IEEE INFOCOM, 1987, pp. 874-881; D. Kowalski and A. Pelc, in APPROX-RANDOM, Lecture Notes in Comput. Sci. 3122, Springer, Berlin, 2004, pp. 171-182]. In this paper we consider the additive approximation ratio of the problem. We prove that there exists a constant c so that the problem cannot be approximated within an additive term of $c\log^2 n$, unless $NP\subseteq BTIME(n^{O(\log\log n)})$.