Bit Complexity of Order Statistics on a Distributed Star Network

We study the bit complexity of order statistics problem on an asynchronous distributed star network. We prove a lower bound ofΩ(N log(LN)) bits for the k-selection problem, and lower bounds of Ω(N log(L − N)) bits for the problems of sorting and ranking. For each of the problems we introduce an algorithm that achieves that bound, thus showing all bounds to be optimal.