Inferring visibility: who's (not) talking to whom?

Consider this simple question: how can a network operator identify the set of routes that pass through its network? Answering this question is surprisingly hard: BGP only informs an operator about a limited set of routes. By observing traffic, an operator can only conclude that a particular route passes through its network -- but not that a route does not pass through its network. We approach this problem as one of statistical inference, bringing varying levels of additional information to bear: (1) the existence of traffic, and (2) the limited set of publicly available routing tables. We show that the difficulty depends critically on the position of the network in the overall Internet topology, and that the operators with the greatest incentive to solve this problem are those for which the problem is hardest. Nonetheless, we show that suitable application of nonparametric inference techniques can solve this problem quite accurately. For certain networks, traffic existence information yields good accuracy, while for other networks an accurate approach uses the "distance" between prefixes, according to a new network distance metric that we define. We then show how solving this problem leads to improved solutions for a particular application: traffic matrix completion.