Deterministic multi-channel information exchange

Abstract

We study the information exchange problem on a set of multiple access channels: k arbitrary nodes have information they want to distribute to the entire network of n nodes via a shared medium partitioned into channels. We devise a deterministic algorithm running in asymptotically optimal time O(k) using O(n log(k)/k) channels if k ≤ 1 6 log n and O(log 1+ρ (n/k)) channels otherwise, where ρ > 0 is an arbitrarily small constant. This is a super-polynomial improvement over the best known bounds [20]. Additionally we show that our results are significantly closer to the optimal solution by proving that Ω(n Ω(1/k) + log k n) channels are necessary to achieve a time complexity of O(k).