Network Topology Tomography

In this work we consider the problem of reconstructing the topology of networks from indirect measurements. A novel algorithm is developed for reconstruction from coocurrence samples—sets of nodes that are known to form a path in the network, but for which the order is unknown. This algorithm outperforms existing algorithms for solving this problem, and is provably optimal in cases where nothing is known a prori about the structure of the network and the signal routing method obeys certain reasonable constraints. The algorithm is efficient in practice, and is found to scale to networks of millions of nodes. The difficultly of network reconstruction from coocurrences is analysed for graphs generated from a variety of random graph models, as well as a number of real world networks. Network structure is found to effect the reconstruction error rate, with scale-free networks resulting in the lowest error. The problem of tree structured coocurrences is also considered. This is the case where the set of nodes in a coocurrence sample form a tree rather than a path in the network. We are not aware of previously published literature on this problem. A restricted form of the problem is proposed, and an algorithm is proposed to solve it. This algorithm can be considered a baseline for other work in this area, as it is simple and computationally efficient. Reconstruction using tree structured coocurrences is found to be harder than for path coocurrences, with higher error rates occurring.