A Centrality Entropy Maximization Problem in Shortest Path Routing Networks

In the context of an IP network, this paper investigates an interesting case of the inverse shortest path problem using the concept of network centrality. For a given network, a special probability distribution, namely the centrality distribution associated with the links of a network can be determined based on the number of the shortest paths passing through each link. An entropy measure for this distribution is defined, and the inverse shortest path problem is formulated in terms of maximizing this entropy. We then obtain a centrality distribution that is as broadly distributed as possible subject to the topology constraints. A maximum entropy distribution signifies the decentralization of the network. An appropriate change in the weight of a link alters the number of the shortest paths that pass through it, thereby modifying the centrality distribution. The idea is to obtain a centrality distribution that maximizes the entropy. This problem is shown to be NP-hard, and a heuristic approach is proposed. An application to handling link failure scenarios in Open Shortest Path First routing is discussed.