Technical Report CS-2006-15

Title: Acyclic Type of Relationships Between Autonomous Systems
Authors: Rami Cohen and Danny Raz
Abstract: The Internet connectivity in the Autonomous System (AS) level reflects the commercial relationship between ASes. A connection between two ASes could be of type customer-provider when one AS is a provider of the other AS, or of type peer-peer, if they are peering ASes. This commercial relationship induces a global hierarchical structure which is a key ingredient in the ability to understand the topological structure of the AS connectivity graph. Unfortunately, it is very difficult to collect data regarding the actual type of the relationships between ASes, and in general this information is not part of the collected AS connectivity data. The Type of Relationship (ToR) problem attempts to address this shortcoming, by inferring the type of relationship between connected ASes based on their routing policies. However, the approaches presented so far are local in nature and do not capture the global hierarchical structure.

In this work we define a novel way to infer this type of relationship from the collected data, taking into consideration both local policies and global hierarchy constrains. We define the Acyclic Type of Relationship AToR problem that captures this global hierarchy and present an efficient algorithm that allows determining if there is a hierarchical assignment without invalid paths. We then show that the related general optimization problem is NP-complete and present a 2/3 approximation algorithm where the objective function is to minimize the total number of local policy mismatch. We support our approach by extensive experiments and simulation results showing that our algorithms classify the type of relationship between ASes much better than all previous algorithms.

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