The present invention is directed to a high speed packet switching network and, in particular to a method and system for minimizing the time to establish a connection between an origin and a destination node. Due to high dynamicity of the traffic on transmission links, it is important to select a routing path according to a fully up-to-date information on all network resources. The simpler approach is to calculate a new path for each new connection request. This solution may be very time consuming because there are as many path selection operations as connection set up operations. On another hand, the calculation of paths based on an exhaustive exploration of the network topology, is a complex operation which may also take an inordinate amount of resources in large networks. Many of connections originated from a network node flow to the same destination network node. It is therefore possible to take a serious benefit in reusing the same already calculated paths for several connections towards the same node. The path calculated at the time the connection is requested is recorded in a Routing Database and updated each time a modification occurs in the network. Furthermore, alternate paths for supporting non-disruptive path switch on failure or preemption, and new paths towards potential destination nodes can be calculated and stored when the connection set up process is idle. These last operations are executed in background with a low processing priority and in absence of connection request.