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We investigate the problem of computing the types of the relationships between Internet Autonomous Systems. We refer to the model introduced by Gao IEEE/ACM Transactions on Networking, 9(6):733-645, 2001 and Subramanian (IEEE Infocom, 2002) 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 approximation algorithms and heuristics based on a novel paradigm and show their effectiveness against publicly available data sets. The experiments provide evidence that our algorithms perform significantly better than state-of-the-art heuristics
Battista et al. (Sun,) studied this question.