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Greedy Routing and Virtual Coordinates for Future Networks Greedy Routing and Virtual Coordinates for Future Networks Inauguraldissertation zur Erlangung der W¨urdeeines Doktors der Philosophie vorgelegt der Philosophisch-Naturwissenschaftlichen Fakult¨at der Universit¨atBasel von Ghazi Bouabene aus Tunesien Basel, 2012 Original document stored on the publication server of the University of Basel edoc.unibas.ch This work is licenced under the agreement Attribution Non-Commercial No Derivatives 2.5 Switzerland. The complete text may be viewed here: creativecommons.org/licenses/by-nc-nd/2.5/ch/deed.en Genehmigt von der Philosophisch-Naturwissenschaftlichen Fakult¨at auf Antrag von Prof. Dr. Christian F. Tschudin, Universit¨atBasel, Dissertationsleiter Prof. Dr. Guy Leduc, Universit´ede Li`ege,Korreferent Basel, den 18.09.2012 Prof. Dr. J¨orgSchibler, Dekan Attribution-Noncommercial-No Derivative Works 2.5 Switzerland You are free: to Share — to copy, distribute and transmit the work Under the following conditions: Attribution. You must attribute the work in the manner specified by the author or licensor (but not in any way that suggests that they endorse you or your use of the work). Noncommercial. You may not use this work for commercial purposes. No Derivative Works. You may not alter, transform, or build upon this work. • For any reuse or distribution, you must make clear to others the license terms of this work. The best way to do this is with a link to this web page. • Any of the above conditions can be waived if you get permission from the copyright holder. • Nothing in this license impairs or restricts the author's moral rights. Your fair dealing and other rights are in no way affected by the above. This is a human-readable summary of the Legal Code (the full license) available in German: http://creativecommons.org/licenses/by-nc-nd/2.5/ch/legalcode.de Disclaimer: The Commons Deed is not a license. It is simply a handy reference for understanding the Legal Code (the full license) — it is a human-readable expression of some of its key terms. Think of it as the user-friendly interface to the Legal Code beneath. This Deed itself has no legal value, and its contents do not appear in the actual license. Creative Commons is not a law firm and does not provide legal services. Distributing of, displaying of, or linking to this Commons Deed does not create an attorney-client relationship. Quelle: http://creativecommons.org/licenses/by-nc-nd/2.5/ch/deed.en Datum: 3.4.2009 Abstract At the core of the Internet, routers are continuously struggling with ever-growing routing and forwarding tables. Although hardware ad- vances do accommodate such a growth, we anticipate new requirements e.g. in data-oriented networking where each content piece has to be referenced instead of hosts, such that current approaches relying on global information will not be viable anymore, no matter the hardware progress. In this thesis, we investigate greedy routing methods that can achieve similar routing performance as today but use much less resources and which rely on local information only. To this end, we add specially crafted name spaces to the network in which virtual coordinates repre- sent the addressable entities. Our scheme enables participating routers to make forwarding decisions using only neighbourhood information, as the overarching pseudo-geometric name space structure already orga- nizes and incorporates \vicinity" at a global level. A first challenge to the application of greedy routing on virtual coordinates to future networks is that of routing dead-ends that are local minima due to the difficulty of consistent coordinates attribu- tion. In this context, we propose a routing recovery scheme based on a multi-resolution embedding of the network in low-dimensional Euclidean spaces. The recovery is performed by routing greedily on a blurrier view of the network. The different network detail-levels are obtained though the embedding of clustering-levels of the graph. When compared with higher-dimensional embeddings of a given network, our method shows a significant diminution of routing failures for similar header and control- state sizes. A second challenge to the application of virtual coordinates and greedy routing to future networks is the support of \customer{provider" as well as \peering" relationships between participants, resulting in a differentiated services environment. Although an application of greedy routing within such a setting would combine two very common fields of today's networking literature, such a scenario has, surprisingly, not been studied so far. In this context we propose two approaches to address this scenario. In a first approach we implement a path-vector protocol similar to that of BGP on top of a greedy embedding of the network. This allows each node to build a spatial map associated with each of its neighbours indicating the accessible regions. Routing is then performed through the use of a decision-tree classifier taking the destination coordinates as input. When applied on a real-world dataset (the CAIDA 2004 AS graph) we demonstrate an up to 40% compression ratio of the routing control information at the network's core as well as a computationally efficient decision process comparable to methods such as binary trees and tries. In a second approach, we take inspiration from consensus-finding in social sciences and transform the three-dimensional distance data struc- ture (where the third dimension encodes the service differentiation) into a two-dimensional matrix on which classical embedding tools can be used. This transformation is achieved by agreeing on a set of constraints on the inter-node distances guaranteeing an administratively-correct greedy routing. The computed distances are also enhanced to encode multipath support. We demonstrate a good greedy routing performance as well as an above 90% satisfaction of multipath constraints when re- lying on the non-embedded obtained distances on synthetic datasets. As various embeddings of the consensus distances do not fully exploit their multipath potential, the use of compression techniques such as transform coding to approximate the obtained distance allows for bet- ter routing performances. Acknowledgements I would like to thank many people who contributed to this work in various ways. First, I would like to thank my advisor Prof. Dr. Christian Tschudin for the exploration freedom he gave me and for his confidence during the years. Also, I would like to thank Dr. Christophe Jelger with whom I had the chance to work during the first years of my Ph.D. Our close collaboration on the ANA EU project was not only fun, but also an occasion to revisit the basics of computer communications, from both a design and a software point of view. A special thanks goes also to Dr. Manolis Sifalakis with whom I had the chance to collaborate during the last years of my Ph.D. His tireless positive thinking helped me concretize many of the ideas presented in this work. I would also like to thank the following colleagues, for some, close friends, for making this journey memorable and fun: Paola Ranaldi, Diego Milano, Marcel L¨uthi, Michael Springmann, Nenad Stojnic, David Adametz, Ihab Al Kabary, Julia Vogt, Matthias Amberg and Filip Brink- mann. Some of the lunch time discussions we had are simply unforget- table. On the private side, I would like to thank Simone Haselier for shar- ing this journey with me, and I am very grateful to my parents and my brothers for their love and caring advice. Contents 1 Introduction 1 1.1 Definition of greedy routing on virtual coordinates . .3 1.2 The power of geometric virtual coordinates . .4 1.2.1 Virtual coordinates as an evolution tool . .5 1.2.2 Applications of virtual coordinates and vector spaces9 1.3 Challenges to the deployment of greedy routing on virtual coordinates in future networks . 11 1.4 Summary of contributions . 14 2 Obtaining Coordinates for Greedy Routing 15 2.1 Theoretical approaches to the problem of virtual coordi- nates attribution . 16 2.1.1 Distance labelling techniques . 16 2.1.2 Geometric Approaches . 20 2.2 Embedding techniques in the networking literature . 36 2.2.1 Tree and hierarchical-based techniques . 37 2.2.2 Distance labelling and compact routing techniques 39 2.2.3 Graph drawing techniques . 40 2.2.4 Lipschitz based techniques . 41 2.2.5 Hyperbolic space techniques . 43 2.2.6 Graph sampling techniques and the revival of trees 44 2.3 Summary . 45 3 on Guaranteeing packet delivery in greedy routing 47 3.1 Introduction . 48 3.2 Greedy Routing Dead-End Problem . 49 3.3 Related work . 53 3.4 A cluster-based approach . 56 vii viii Contents 3.4.1 Construction of a cluster graph . 58 3.4.2 Cluster graph embedding . 59 3.4.3 Cluster-level state . 60 3.4.4 Operation of greedy routing . 61 3.4.5 Multiple cluster levels . 62 3.5 Evaluation . 63 3.5.1 Experimental set-up . 63 3.5.2 Clustering algorithm used for the tests . 64 3.5.3 Greedy routing performance . 64 3.5.4 State overhead for clustering . 69 3.6 Discussion . 70 3.6.1 On the general effects of clustering . 70 3.6.2 Clustering versus inter-domain routing . 72 3.7 Conclusion . 73 4 Greedy Routing and administrative policies 75 4.1 Introduction . 76 4.2 Administrative relationships and policies . 77 4.2.1 Security policies . 78 4.2.2 Traffic policies . 78 4.2.3 Administrative relationships and policies . 78 4.3 Administrative policies and future networks . 82 4.3.1 Administrative policies and greedy routing . 82 4.4 The problem from a graph viewpoint . 85 4.4.1 Relation to social sciences and Cognitive Social Structures . 88 4.5 Understanding the problem from a distance matrix view- point............................
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