An entropy maximization problem in shortest path routing networks

TLDR: In the context of an IP network, an interesting case of the inverse shortest path problem is investigated using the concept of network centrality, and a heuristic approach is proposed to obtain a centrality distribution that maximizes the entropy.

Abstract: In the context of an IP network, we investigate an interesting case of the inverse shortest path problem using the concept of network centrality. For a given network, the centrality distribution associated with the links of a network can be determined based on the number of shortest paths passing through each link. An entropy measure for this distribution is defined, and we then forumulate the inverse shortest problem in terms of maximizing this entropy. We then obtain a centrality distribution that is as broadly distributed as possible subject to the topology constraints. An appropriate change in the weight of a link alters the number of 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.