Misleading Stars: What Cannot Be Measured in the Internet?
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.
KeywordsShort Path Star Graph Proper Coloring Chromatic Polynomial Connected Topology
Unable to display preview. Download preview PDF.
- 4.Alon, N., Emek, Y., Feldman, M., Tennenholtz, M.: Economical graph discovery. In: Proc. 2nd Symposium on Innovations in Computer Science, ICS (2011)Google Scholar
- 5.Anandkumar, A., Hassidim, A., Kelner, J.: Topology discovery of sparse random graphs with few participants. In: Proc. SIGMETRICS (2011)Google Scholar
- 6.Augustin, B., Cuvellier, X., Orgogozo, B., Viger, F., Friedman, T., Latapy, M., Magnien, C., Teixeira, R.: Avoiding traceroute anomalies with paris traceroute. In: Proc. 6th ACM SIGCOMM Conference on Internet Measurement (IMC), pp. 153–158 (2006)Google Scholar
- 7.Buchanan, M.: Data-bots chart the internet. Science 813(3) (2005)Google Scholar
- 8.Cheswick, B., Burch, H., Branigan, S.: Mapping and visualizing the internet. In: Proc. USENIX Annual Technical Conference, ATEC (2000)Google Scholar
- 9.Faloutsos, M., Faloutsos, P., Faloutsos, C.: On power-law relationships of the internet topology. In: Proc. SIGCOMM, pp. 251–262 (1999)Google Scholar
- 10.Gunes, M., Sarac, K.: Resolving anonymous routers in internet topology measurement studies. In: Proc. INFOCOM (2008)Google Scholar
- 12.Labovitz, C., Ahuja, A., Venkatachary, S., Wattenhofer, R.: The impact of internet policy and topology on delayed routing convergence. In: Proc. 20th Annual Joint Conference of the IEEE Computer and Communications Societies, INFOCOM (2001)Google Scholar
- 13.Paul, S., Sabnani, K.K., Lin, J.C., Bhattacharyya, S.: Reliable multicast transport protocol (rmtp). IEEE Journal on Selected Areas in Communications 5(3) (1997)Google Scholar
- 14.Poese, I., Frank, B., Ager, B., Smaragdakis, G., Feldmann, A.: Improving content delivery using provider-aided distance information. In: Proc. ACM IMC (2010)Google Scholar
- 15.Tangmunarunkit, H., Govindan, R., Shenker, S., Estrin, D.: The impact of routing policy on internet paths. In: Proc. INFOCOM, vol. 2, pp. 736–742 (2002)Google Scholar
- 16.Yao, B., Viswanathan, R., Chang, F., Waddington, D.: Topology inference in the presence of anonymous routers. In: Proc. IEEE INFOCOM, pp. 353–363 (2003)Google Scholar