The private network-to-network interface (PNNI) protocol, which specifies how topology information is to be distributed in an ATM network, allows ATM switches to be aggregated into clusters railed peer groups. Outside of a peer group its topology is aggregated into a single logical node. This method ran be applied recursively so that PNNI can hierarchically aggregate network topology state information, To provide good accuracy in choosing optimal paths in a PNNI network, the PNNI standard provides a way to represent a peer group with a structure called the complex node representation. It allows the cost of traversing the peer group between any ingress and egress to be advertised in a compact form, Complex node representations using a small number of links result in a correspondingly short path computation time and therefore in good performance, It is, therefore, desirable that the complex node representation contains as few links as possible. This paper considers the class of complex node representations for which the path computation time is minimal. It assumes that the path selection is based on restrictive costs, such as bandwidth, and considers the symmetric case. It presents a method for constructing the set of the optimal complex node representations in the sense that they use the minimum possible number of links. Central to the development of this method is the establishment of the optimal substructure property of the optimal complex node representations.
