Networks Cannot Compute Their Diameter in Sublinear Time [chapter]

Silvio Frischknecht, Stephan Holzer, Roger Wattenhofer
2012 Proceedings of the Twenty-Third Annual ACM-SIAM Symposium on Discrete Algorithms  
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 anΩ(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 − ε)-approximation
more » ... − ε)-approximation of the diameter requiresΩ( √ n + D) rounds. Furthermore we use our new technique to prove anΩ( √ n + D) lower bound on approximating the girth of a graph by a factor 2 − ε. 1. Alice collects the messages M a (r) that nodes in V a wanted to send over edges in C k while executing A and sends M a (r) to Bob using their communication channel.
doi:10.1137/1.9781611973099.91 dblp:conf/soda/FrischknechtHW12 fatcat:4p374ytu7zgjvfebwnw3gib4gy