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Misleading Stars: What Cannot Be Measured in the Internet?

  • Yvonne Anne Pignolet
  • Stefan Schmid
  • Gilles Tredan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6950)

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.

Keywords

Short Path Star Graph Proper Coloring Chromatic Polynomial Connected Topology 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Yvonne Anne Pignolet
    • 1
  • Stefan Schmid
    • 2
  • Gilles Tredan
    • 2
  1. 1.ABB ResearchSwitzerland
  2. 2.TU Berlin & T-LabsGermany

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