text: The type of business relationships between the Internet autonomous systems (AS) determines the BGP inter-domain routing. Previous works on inferring AS relationships relied on the connectivity information between ASes. In this paper we infer AS relationships by analysing the routing polices of ASes encoded in the BGP attributes Communities and the Locpref. We accumulate BGP data from RouteViews, RIPE RIS and the public Route Servers in August 2010 and February 2011. Based on the routing policies extracted from data of the two BGP attributes, we obtain AS relationships for 39 links in our data, which include all links among the Tier-1 ASes and most links between Tier-1 and Tier-2 ASes. We also reveal a number of special AS relationships, namely the hybrid relationship, the partial-transit relationship, the indirect peering relationship and the backup links. These special relationships are relevant to a better understanding of the Internet routing. Our work provides a profound methodological progress for inferring the AS relationships.
  @cite_31: 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 mismatches. 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.
  @cite_4: An experimental study of the feasibility and accuracy of the acyclicity approach introduced in [14] for the inference of business relationships among autonomous systems (ASes) is provided. We investigate the maximum acyclic type-of-relationship problem: on a given set of AS paths, find a maximum-cardinality subset which allows an acyclic and valley-free orientation. Inapproximability and NP-hardness results for this problem are presented and a heuristic is designed. The heuristic is experimentally compared to most of the state-of-the-art algorithms on a reliable data set. It turns out that the proposed heuristic produces the least number of misclassified customer-to-provider relationships among the tested algorithms. Moreover, it is flexible in handling pre-knowledge in the sense that already a small amount of correct relationships is enough to produce a high-quality relationship classification. Furthermore, the reliable data set is used to validate the acyclicity assumptions. The findings demonstrate that acyclicity notions should be an integral part of models of AS relationships.
summary: In @cite_31 the Acyclic Type of Relationship (AToR) problem is defined. According to AToR when p2c relationships are assigned a directed edge, the resulting AS graph should be acyclic. In @cite_4 the authors validate the acyclicity of the AS graph and propose a heuristic to solve the maximal AToR problem.