Abstract
We contribute to the study of inferring commercial relationships between autonomous systems (AS relationships) from observable BGP routes. We deduce several forbidden patterns of AS relationships that impose a certain type of acyclicity on the AS graph. We investigate algorithms for solving the acyclic all-paths type-of-relationship problem, i.e., given a set of AS paths, find an orientation of the edges according to some types of AS relationships such that the oriented AS graph is acyclic (with respect to the forbidden patterns) and all AS paths are valley-free. As possible AS relationships we include customer-to-provider, peer-to-peer, and sibling-to-sibling. Moreover, we examine a number of problem versions parameterized by sets K and U where K is the set of edge types available for describing explicit pre-knowledge and U is the set of edge types available for completion of partial orientations. A complete complexity classification of all 56 cases (8 type sets for pre-knowledge and 7 type sets for completion) is given. The most relevant practical result is a linear-time algorithm for finding an acyclic and valley-free completion using customer-to-provider relations given any kind of pre-knowledge. Interestingly, if we allow sibling-to-sibling relations for completions then most of the non-trivial inference problems become NP-hard.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Chang, H., Govindan, R., Jamin, S., Shenker, S.J., Willinger, W.: Towards capturing representative AS-level Internet topologies. Comput. Netw. 44(6), 737–755 (2004)
Di Battista, G., Erlebach, T., Hall, A., Patrignani, M., Pizzonia, M., Schank, T.: Computing the types of the relationships between autonomous systems. IEEE/ACM Trans. Networking (to appear)
Dimitropoulos, X.A., Krioukov, D.V., Huffaker, B., claffy, k., Riley, G.F.: Inferring AS relationships: Dead end or lively beginning? In: Nikoletseas, S.E. (ed.) WEA 2005. LNCS, vol. 3503, pp. 113–125. Springer, Heidelberg (2005)
Gao, L.: On inferring autonomous system relationships in the Internet. IEEE/ACM Trans. Networking 9(6), 733–745 (2001)
Gao, L., Rexford, J.: Stable Internet routing without global coordination. IEEE/ACM Trans. Networking 9(6), 681–692 (2001)
Govindan, R., Reddy, A.: An analysis of Internet inter-domain topology and route stability. In: Proc. 16th Joint Conference of the IEEE Computer and Communications Societies (INFOCOM 1997), pp. 850–857. IEEE, Los Alamitos (1997)
Griffin, T.G., Wilfong, G.T.: An analysis of BGP convergence properties. Comput. Commun. Rev. 29(4), 277–288 (1999)
Kosub, S., Maaß, M.G., Täubig, H.: Acyclic type-of-relationship problems on the Internet. Technical Report TUM-I0605, Fakultät für Informatik, Technische Universität München (March 2006)
Labovitz, C., Ahuja, A., Wattenhofer, R., Venkatachary, S.: The impact of Internet policy and topology on delayed routing convergence. In: Proc. 20th Joint Conference of the IEEE Computer and Communications Societies (INFOCOM 2001), pp. 537–546. IEEE, Los Alamitos (2001)
Norton, W.B.: Internet Service Providers and peering. Equinix White Paper, Equinix, Inc. (2001)
Siganos, G., Faloutsos, M.: Analyzing BGP policies: Methodology and tool. In: Proc. 23rd Joint Conference of the IEEE Computer and Communications Societies (INFOCOM 2004), pp. 1640–1651. IEEE, Los Alamitos (2004)
Subramanian, L., Agarwal, S., Rexford, J., Katz, R.H.: Characterizing the Internet hierarchy from multiple vantage points. In: Proc. 21st Joint Conference of the IEEE Computer and Communications Societies (INFOCOM 2002), pp. 618–627. IEEE, Los Alamitos (2002)
Tangmunarunkit, H., Doyle, J., Govindan, R., Jamin, S., Shenker, S.J., Willinger, W.: Does AS size determine degree in AS topology? Comput. Commun. Rev. 31(5), 7–10 (2001)
Tangmunarunkit, H., Govindan, R., Shenker, S., Estrin, D.: The impact of routing policy on Internet paths. In: Proc. 20th Joint Conference of the IEEE Computer and Communications Societies (INFOCOM 2001), pp. 736–742. IEEE, Los Alamitos (2001)
van Beijnum, I.: BGP. O’Reilly & Associates, Sebastopol (2002)
Xia, J., Gao, L.: On the evaluation of AS relationship inferences. In: Proc. 47th IEEE Global Telecommunications Conference (Globecom 2004), vol. 3, pp. 1373–1377. IEEE, Los Alamitos (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kosub, S., Maaß, M.G., Täubig, H. (2006). Acyclic Type-of-Relationship Problems on the Internet. In: Erlebach, T. (eds) Combinatorial and Algorithmic Aspects of Networking. CAAN 2006. Lecture Notes in Computer Science, vol 4235. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11922377_9
Download citation
DOI: https://doi.org/10.1007/11922377_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-48822-4
Online ISBN: 978-3-540-48824-8
eBook Packages: Computer ScienceComputer Science (R0)