The discovery of Autonomous Systems (ASes) interconnections and the inference of their commercial Type-of-Relationships (ToR) has been extensively studied during the last few years. The main motivation is to accurately calculate AS-level paths and to provide better topological view of the Internet. An inherent problem in current algorithms is their extensive use of heuristics. Such heuristics incur unbounded errors which are spread over all inferred relationships. We propose a near-deterministic algorithm for solving the ToR inference problem. Our algorithm uses as input the Internet core, which is a dense sub-graph of top-level ASes. We test several methods for creating such a core and demonstrate the robustness of the algorithm to the core's size and density, the inference period, and errors in the core. We evaluate our algorithm using AS-level paths collected from RouteViews BGP paths and DIMES traceroute measurements. Our proposed algorithm deterministically infers over 95 of the approximately 58,000 AS topology links. The inference becomes stable when using a week worth of data and as little as 20 ASes in the core. The algorithm infers 2-3 times more peer-to-peer relationships in edges discovered only by DIMES than in RouteViews edges, validating the DIMES promise to discover periphery AS edges.
Battista al @cite_16 showed that the decision version of the ToR problem () is an NP-complete problem in the general case. Motivated by the hardness of the general problem, they proposed approximation algorithms and reduced the ToR-D problem to a 2SAT formula by mapping any two adjacent edges in all input AS-level routing paths into a clause with two literals, while adding heuristics based inference.
@cite_16
2130725804
The problem of computing the types of the relationships between Internet autonomous systems is investigated. We refer to the model introduced in (ref.1), (ref.2) that bases the discovery of such relationships on the analysis of the AS paths extracted from the BGP routing tables. We characterize the time complexity of the above problem, showing both NP-completeness results and efficient algorithms for solving specific cases. Motivated by the hardness of the general problem, we propose heuristics based on a novel paradigm and show their effectiveness against publicly available data sets. The experiments put in evidence that our heuristics performs significantly better than state of the art heuristics.