Theoretical Computer Science ( IF 0.747 ) Pub Date : 2020-08-18 , DOI: 10.1016/j.tcs.2020.07.032
We consider the aggregation problem in radio networks: find a spanning tree in a given graph and a conflict-free schedule of the edges so as to minimize the latency of the computation. While a large body of literature exists on this and related problems, we give the first approximation results in graphs that are not induced by unit ranges in the plane. We give a polynomial-time $\stackrel{˜}{\mathrm{O}}\left(\sqrt{dn}\right)$-approximation algorithm, where d is the average degree and n the number of vertices in the graph, and show that the problem is $\mathrm{\Omega }\left({n}^{1-ϵ}\right)$-hard (and $\mathrm{\Omega }\left({\left(dn\right)}^{1/2-ϵ}\right)$-hard) to approximate even on bipartite graphs, for any $ϵ>0$, rendering our algorithm essentially optimal. We also obtain a $O\left(\mathrm{log}n\right)$-approximation in interval graphs.