# Networks Cannot Compute Their Diameter in Sublinear Time

## Silvio Frischknecht, Stephan Holzer and Roger Wattenhofer

Abstract:
We study the problem of computing the diameter of a network in a distributed way. The model of distributed computation we consider is: in each synchronous round, each node can transmit a different (but) short message to each of its neighbors. We provide an $\tilde{O}(n)$ lower bound for the number of communication rounds needed, where n denotes the number of nodes in the network. This lower bound is valid even if the diameter of the network is a small constant. We also show that a $(3/2-\epsilon)$-approximation of the diameter requires $\tilde{\Omega}(\sqrt{n} +D)$ rounds. Furthermore we use our new technique to prove an $\tilde{\Omega}(\sqrt{n} +D)$ lower bound on approximating the girth of a graph by a factor
$2-\epsilon$.

Guest: Stephan Holzer
Host: Chen Avin