Theoretical Computer Science Radio Aggregation Scheduling I

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 Õ( √ dn)approximation algorithm, where d is the average degree and n the number of vertices in the graph, and show that the problem is Ω(n1− )-hard (and Ω((dn)1/2− )-hard) to approximate even on bipartite graphs, for any > 0, rendering our algorithm essentially optimal. We also obtain a O(log n)-approximation in interval graphs.