Computing giant graph diameters

Paper in proceeding, 2016

This paper is devoted to the fast and exact diameter computation in graphs with n vertices and m edges, if the diameter is a large fraction of n. We give an optimal O(m+n) time algorithm for diameters above n/2. The problem changes its structure at diameter value n/2, as large cycles may be present. We propose a randomized O(m+n log n) time algorithm for diameters above n/3.