A routing scheme for an ATM switching network includes a plurality of switching nodes, each of which includes individual storage for storing routing messages for each outgoing link. A call at a source node is routed through one possible routing path which requires only one or two links to complete a connection to a destination node. In such case, one of the routing paths is selected based on link state information concerning only the possible routing paths. If the call requires a route path which includes three or more links to the destination node, the source node performs a predefined sequential routing to its neighboring node before the neighboring node negotiates with selected intermediate nodes for a connection involving two links. The routing messages stored at each node are processed independently and simultaneously by each node. The main requirement is that routing decisions must be based on true link-state information. A protocol is devised for fast and efficient bulk processing while avoiding protential deadlocks.