  In this paper we address several network design, clustering and Quality of
Service (QoS) optimization problems and present novel, efficient, offline
algorithms which compute optimal or near-optimal solutions. The QoS
optimization problems consist of reliability improvement (by computing backup
shortest paths) and network link upgrades (in order to reduce the latency on
several paths). The network design problems consist of determining small
diameter networks, as well as very well connected and regular network
topologies. The network clustering problems consider only the restricted model
of static and mobile path networks, for which we were able to develop optimal
algorithms.
