Recovering Euclidean Distance Matrices via Landmark MDS

In network topology discovery, it is often necessary to collect measurements between network elements without injecting large amounts of traffic into the network. A possible solution to this problem is to actively query the network for some measurements and use these to infer the remaining ones. We frame this as a particular version of the Noisy Matrix Completion problem where the entries reflect path-level measurements (distances) between network elements, and we study a variant of the Landmark MDS algorithm proposed in [9] and [16]. This algorithm finds an Euclidean embedding of the network elements that preserves distances, given that we observe all pairwise distances between a small set of landmark nodes and only few distances between the landmarks and the remaining nodes (end hosts). We give a theoretical analysis of Landmark MDS, specifically showing that without noise, the algorithm perfectly recovers all pairwise distances, and bounding the reconstruction error in the presence of noise.