Scalable Routing Easy as PIE: a Practical Isometric Embedding Protocol (Technical Report)

We present PIE, a scalable routing scheme that achieves 100% packet delivery and low path stretch. It is easy to implement in a distributed fashion and works well when costs are associated to links. Scalability is achieved by using virtual coordinates in a space of concise dimensionality, which enables greedy routing based only on local knowledge. PIE is a general routing scheme, meaning that it works on any graph. We focus however on the Internet, where routing scalability is an urgent concern. We show analytically and by using simulation that the scheme scales extremely well on Internet-like graphs. In addition, its geometric nature allows it to react efficiently to topological changes or failures by finding new paths in the network at no cost, yielding better delivery ratios than standard algorithms. The proposed routing scheme needs an amount of memory polylogarithmic in the size of the network and requires only local communication between the nodes. Although each node constructs its coordinates and routes packets locally, the path stretch remains extremely low, even lower than for centralized or less scalable state-of-the-art algorithms: PIE always finds short paths and often enough finds the shortest paths.Comment: This work has been previously published in IEEE ICNP'11. The present document contains an additional optional mechanism, presented in Section III-D, to further improve performance by using route asymmetry. It also contains new simulation result

Robust geometric forest routing with tunable load balancing

Although geometric routing is proposed as a memory-efficient alternative to traditional lookup-based routing and forwarding algorithms, it still lacks: i) adequate mechanisms to trade stretch against load balancing, and ii) robustness to cope with network topology change. The main contribution of this paper involves the proposal of a family of routing schemes, called Forest Routing. These are based on the principles of geometric routing, adding flexibility in its load balancing characteristics. This is achieved by using an aggregation of greedy embeddings along with a configurable distance function. Incorporating link load information in the forwarding layer enables load balancing behavior while still attaining low path stretch. In addition, the proposed schemes are validated regarding their resilience towards network failures

Graph embeddings for low-stretch greedy routing

The simplest greedy geometric routing forwards packets to make most progress in terms of geometric distance within reach. Its notable advantages are low complexity, and the use of local information only. However, two problems of greedy routing are that delivery is not always guaranteed, and that the greedy routes may take more hops than the corresponding shortest paths. Additionally, in dynamic multihop networks, routing elements can join or leave during network operation or exhibit intermittent failures. Even a single link or node removal may invalidate the greedy routing success guarantees. Greedy embedding is a graph embedding that makes the simple greedy packet forwarding successful for every source-destination pair. In this dissertation, we consider the problems of designing greedy graph embeddings that also yield low hop stretch of the greedy paths over the shortest paths and can accommodate network dynamics. In the first part of the dissertation, we consider embedding and routing for arbitrary unweighted network graphs, based on greedy routing and utilizing virtual node coordinates. We propose an algorithm for online greedy graph embedding in the hyperbolic plane that enables incremental embedding of network nodes as they join the network, without disturbing the global embedding. As an alternative to frequent reembedding of temporally dynamic network graphs in order to retain the greedy embedding property, we propose a simple but robust generalization of greedy geometric routing called Gravity--Pressure (GP) routing. Our routing method always succeeds in finding a route to the destination provided that a path exists, even if a significant fraction of links or nodes is removed subsequent to the embedding. GP routing does not require precomputation or maintenance of special spanning subgraphs and is particularly suitable for operation in tandem with our proposed algorithm for online graph embedding. In the second part of the dissertation we study how topological and geometric properties of embedded graphs influence the hop stretch. Based on the obtained insights, we synthesize embedding heuristics that yield minimal hop stretch greedy embeddings. Finally, we verify their effectiveness on models of synthetic graphs as well as instances of several classes of real-world network graphs

Hyperbolic Geometry of Complex Networks

We develop a geometric framework to study the structure and function of complex networks. We assume that hyperbolic geometry underlies these networks, and we show that with this assumption, heterogeneous degree distributions and strong clustering in complex networks emerge naturally as simple reflections of the negative curvature and metric property of the underlying hyperbolic geometry. Conversely, we show that if a network has some metric structure, and if the network degree distribution is heterogeneous, then the network has an effective hyperbolic geometry underneath. We then establish a mapping between our geometric framework and statistical mechanics of complex networks. This mapping interprets edges in a network as non-interacting fermions whose energies are hyperbolic distances between nodes, while the auxiliary fields coupled to edges are linear functions of these energies or distances. The geometric network ensemble subsumes the standard configuration model and classical random graphs as two limiting cases with degenerate geometric structures. Finally, we show that targeted transport processes without global topology knowledge, made possible by our geometric framework, are maximally efficient, according to all efficiency measures, in networks with strongest heterogeneity and clustering, and that this efficiency is remarkably robust with respect to even catastrophic disturbances and damages to the network structure

Greedy routing and virtual coordinates for future networks

At the core of the Internet, routers are continuously struggling with ever-growing routing and forwarding tables. Although hardware advances 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 represent 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 organizes 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 attribution. 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 structure (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 relying 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 better routing performances

Analyzing and Enhancing Routing Protocols for Friend-to-Friend Overlays

The threat of surveillance by governmental and industrial parties is more eminent than ever. As communication moves into the digital domain, the advances in automatic assessment and interpretation of enormous amounts of data enable tracking of millions of people, recording and monitoring their private life with an unprecedented accurateness. The knowledge of such an all-encompassing loss of privacy affects the behavior of individuals, inducing various degrees of (self-)censorship and anxiety. Furthermore, the monopoly of a few large-scale organizations on digital communication enables global censorship and manipulation of public opinion. Thus, the current situation undermines the freedom of speech to a detrimental degree and threatens the foundations of modern society. Anonymous and censorship-resistant communication systems are hence of utmost importance to circumvent constant surveillance. However, existing systems are highly vulnerable to infiltration and sabotage. In particular, Sybil attacks, i.e., powerful parties inserting a large number of fake identities into the system, enable malicious parties to observe and possibly manipulate a large fraction of the communication within the system. Friend-to-friend (F2F) overlays, which restrict direct communication to parties sharing a real-world trust relationship, are a promising countermeasure to Sybil attacks, since the requirement of establishing real-world trust increases the cost of infiltration drastically. Yet, existing F2F overlays suffer from a low performance, are vulnerable to denial-of-service attacks, or fail to provide anonymity. Our first contribution in this thesis is concerned with an in-depth analysis of the concepts underlying the design of state-of-the-art F2F overlays. In the course of this analysis, we first extend the existing evaluation methods considerably, hence providing tools for both our and future research in the area of F2F overlays and distributed systems in general. Based on the novel methodology, we prove that existing approaches are inherently unable to offer acceptable delays without either requiring exhaustive maintenance costs or enabling denial-of-service attacks and de-anonymization. Consequentially, our second contribution lies in the design and evaluation of a novel concept for F2F overlays based on insights of the prior in-depth analysis. Our previous analysis has revealed that greedy embeddings allow highly efficient communication in arbitrary connectivity-restricted overlays by addressing participants through coordinates and adapting these coordinates to the overlay structure. However, greedy embeddings in their original form reveal the identity of the communicating parties and fail to provide the necessary resilience in the presence of dynamic and possibly malicious users. Therefore, we present a privacy-preserving communication protocol for greedy embeddings based on anonymous return addresses rather than identifying node coordinates. Furthermore, we enhance the communication’s robustness and attack-resistance by using multiple parallel embeddings and alternative algorithms for message delivery. We show that our approach achieves a low communication complexity. By replacing the coordinates with anonymous addresses, we furthermore provably achieve anonymity in the form of plausible deniability against an internal local adversary. Complementary, our simulation study on real-world data indicates that our approach is highly efficient and effectively mitigates the impact of failures as well as powerful denial-of-service attacks. Our fundamental results open new possibilities for anonymous and censorship-resistant applications.Die Bedrohung der Überwachung durch staatliche oder kommerzielle Stellen ist ein drängendes Problem der modernen Gesellschaft. Heutzutage findet Kommunikation vermehrt über digitale Kanäle statt. Die so verfügbaren Daten über das Kommunikationsverhalten eines Großteils der Bevölkerung in Kombination mit den Möglichkeiten im Bereich der automatisierten Verarbeitung solcher Daten erlauben das großflächige Tracking von Millionen an Personen, deren Privatleben mit noch nie da gewesener Genauigkeit aufgezeichnet und beobachtet werden kann. Das Wissen über diese allumfassende Überwachung verändert das individuelle Verhalten und führt so zu (Selbst-)zensur sowie Ängsten. Des weiteren ermöglicht die Monopolstellung einiger weniger Internetkonzernen globale Zensur und Manipulation der öffentlichen Meinung. Deshalb stellt die momentane Situation eine drastische Einschränkung der Meinungsfreiheit dar und bedroht die Grundfesten der modernen Gesellschaft. Systeme zur anonymen und zensurresistenten Kommunikation sind daher von ungemeiner Wichtigkeit. Jedoch sind die momentanen System anfällig gegen Sabotage. Insbesondere ermöglichen es Sybil-Angriffe, bei denen ein Angreifer eine große Anzahl an gefälschten Teilnehmern in ein System einschleust und so einen großen Teil der Kommunikation kontrolliert, Kommunikation innerhalb eines solchen Systems zu beobachten und zu manipulieren. F2F Overlays dagegen erlauben nur direkte Kommunikation zwischen Teilnehmern, die eine Vertrauensbeziehung in der realen Welt teilen. Dadurch erschweren F2F Overlays das Eindringen von Angreifern in das System entscheidend und verringern so den Einfluss von Sybil-Angriffen. Allerdings leiden die existierenden F2F Overlays an geringer Leistungsfähigkeit, Anfälligkeit gegen Denial-of-Service Angriffe oder fehlender Anonymität. Der erste Beitrag dieser Arbeit liegt daher in der fokussierten Analyse der Konzepte, die in den momentanen F2F Overlays zum Einsatz kommen. Im Zuge dieser Arbeit erweitern wir zunächst die existierenden Evaluationsmethoden entscheidend und erarbeiten so Methoden, die Grundlagen für unsere sowie zukünftige Forschung in diesem Bereich bilden. Basierend auf diesen neuen Evaluationsmethoden zeigen wir, dass die existierenden Ansätze grundlegend nicht fähig sind, akzeptable Antwortzeiten bereitzustellen ohne im Zuge dessen enorme Instandhaltungskosten oder Anfälligkeiten gegen Angriffe in Kauf zu nehmen. Folglich besteht unser zweiter Beitrag in der Entwicklung und Evaluierung eines neuen Konzeptes für F2F Overlays, basierenden auf den Erkenntnissen der vorangehenden Analyse. Insbesondere ergab sich in der vorangehenden Evaluation, dass Greedy Embeddings hoch-effiziente Kommunikation erlauben indem sie Teilnehmer durch Koordinaten adressieren und diese an die Struktur des Overlays anpassen. Jedoch sind Greedy Embeddings in ihrer ursprünglichen Form nicht auf anonyme Kommunikation mit einer dynamischen Teilnehmermengen und potentiellen Angreifern ausgelegt. Daher präsentieren wir ein Privätssphäre-schützenden Kommunikationsprotokoll für F2F Overlays, in dem die identifizierenden Koordinaten durch anonyme Adressen ersetzt werden. Des weiteren erhöhen wir die Resistenz der Kommunikation durch den Einsatz mehrerer Embeddings und alternativer Algorithmen zum Finden von Routen. Wir beweisen, dass unser Ansatz eine geringe Kommunikationskomplexität im Bezug auf die eigentliche Kommunikation sowie die Instandhaltung des Embeddings aufweist. Ferner zeigt unsere Simulationstudie, dass der Ansatz effiziente Kommunikation mit kurzen Antwortszeiten und geringer Instandhaltungskosten erreicht sowie den Einfluss von Ausfälle und Angriffe erfolgreich abschwächt. Unsere grundlegenden Ergebnisse eröffnen neue Möglichkeiten in der Entwicklung anonymer und zensurresistenter Anwendungen

Dynamics of spectral algorithms for distributed routing

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2012.Cataloged from PDF version of thesis.Includes bibliographical references (p. 109-117).In the past few decades distributed systems have evolved from man-made machines to organically changing social, economic and protein networks. This transition has been overwhelming in many ways at once. Dynamic, heterogeneous, irregular topologies have taken the place of static, homogeneous, regular ones. Asynchronous, ad hoc peer-to-peer networks have replaced carefully engineered super-computers, governed by globally synchronized clocks. Modern network scales have demanded distributed data structures in place of traditionally centralized ones. While the core problems of routing remain mostly unchanged, the sweeping changes of the computing environment invoke an altogether new science of algorithmic and analytic techniques. It is these techniques that are the focus of the present work. We address the re-design of routing algorithms in three classical domains: multi-commodity routing, broadcast routing and all-pairs route representation. Beyond their practical value, our results make pleasing contributions to Mathematics and Theoretical Computer Science. We exploit surprising connections to NP-hard approximation, and we introduce new techniques in metric embeddings and spectral graph theory. The distributed computability of "oblivious routes", a core combinatorial property of every graph and a key ingredient in route engineering, opens interesting questions in the natural and experimental sciences as well. Oblivious routes are "universal" communication pathways in networks which are essentially unique. They are magically robust as their quality degrades smoothly and gracefully with changes in topology or blemishes in the computational processes. While we have only recently learned how to find them algorithmically, their power begs the question whether naturally occurring networks from Biology to Sociology to Economics have their own mechanisms of finding and utilizing these pathways. Our discoveries constitute a significant progress towards the design of a self-organizing Internet, whose infrastructure is fueled entirely by its participants on an equal citizen basis. This grand engineering challenge is believed to be a potential technological solution to a long line of pressing social and human rights issues in the digital age. Some prominent examples include non-censorship, fair bandwidth allocation, privacy and ownership of social data, the right to copy information, non-discrimination based on identity, and many others.by Petar Maymounkov.Ph.D

Fault-tolerant Greedy Forest Routing for complex networks

Geometric routing has been proposed in literature as a memory-efficient alternative to traditional lookup-based routing and forwarding algorithms. However, existing geometric routing schemes lack the ability to address network link and node failures in a natural way, while maintaining a low path stretch. The main contribution of this paper is a novel routing scheme called Greedy Forest Routing (GFR) based on the principles of geometric routing. By employing a graph embedding based on low-redundancy spanning trees, its fault-tolerant characteristics are enhanced. Using a multi-dimensional tree embedding enables natural traffic redirection while still attaining a low average hop count