# Faster swap edge computation in minimum diameter spanning trees

## Abstract

In network communication systems, frequently messages are routed along a minimum diameter spanning tree (MDST) of the network, to minimize the maximum travel time of messages. When a transient failure disables an edge of the MDST, the network is disconnected, and a temporary replacement edge must be chosen, which should ideally minimize the diameter of the new spanning tree. Such a replacement edge is called a best swap. Preparing for the failure of any edge of the MDST, the all-best-swaps (ABS) problem asks for finding the best swap for every edge of the MDST. Given a 2-edge-connected weighted graph G=(V,E), where |V|=n and |E|=m, we solve the ABS problem in O(mlog∈n) time and O(m) space, thus considerably improving upon the decade-old previously best solution, which requires $O(n\sqrt m )$ time and O(m) space, for m=o(n 2/log∈ 2 n). © 2010 Springer Science+Business Media, LLC.