Misleading stars: what cannot be measured in the internet?

Abstract

Abstract. Traceroute measurements are one of the main instruments to shed light onto the structure and properties of today's complex networks such as the Internet. This paper studies the feasibility and infeasibility of inferring the network topology given traceroute data from a worst-case perspective, i.e., without any probabilistic assumptions on, e.g., the nodes' degree distribution. We attend to a scenario where some of the routers are anonymous, and propose two fundamental axioms that model two basic assumptions on the traceroute data: (1) each trace corresponds to a real path in the network, and (2) the routing paths are at most a factor 1/α off the shortest paths, for some parameter α ∈ (0, 1]. In contrast to existing literature that focuses on the cardinality of the set of (often only minimal) inferrable topologies, we argue that a large number of possible topologies alone is often unproblematic, as long as the networks have a similar structure. We hence seek to characterize the set of topologies inferred with our axioms. We introduce the notion of star graphs whose colorings capture the differences among inferred topologies; it also allows us to construct inferred topologies explicitly. We find that in general, inferrable topologies can differ significantly in many important aspects, such as the nodes' distances or the number of triangles. These negative results are complemented by a discussion of a scenario where the trace set is best possible, i.e., "complete". It turns out that while some properties such as the node degrees are still hard to measure, a complete trace set can help to determine global properties such as the connectivity.

Adversarial topology discovery in network virtualization environments: a threat for ISPs?

“…The classic instrument to discover Internet topologies is traceroute [7], but the tool has several problems which renders the problem challenging. One complication of traceroute stems from the fact that routers may appear as stars (i.e., anonymous nodes), which renders the accurate characterization of Internet topologies difficult [1,23,30]. Network tomography is another important field of topology discovery.…”

Request Complexity of VNet Topology Extraction: Dictionary-Based Attacks

“…The classic instrument to discover Internet topologies is traceroute [4], but the tool has several problems which makes the problem challenging. One complication of traceroute stems from the fact that routers may appear as stars (i.e., anonymous nodes), which renders the accurate characterization of Internet topologies difficult [1,10,13]. Network tomography is another important field of topology discovery.…”