Greedy Forwarding in Dynamic Scale-Free Networks Embedded in Hyperbolic Metric Spaces

Papadopoulos, Fragkiskos; Krioukov, Dmitri; Boguñá, Marián; Vahdat, Amin

doi:10.1109/infcom.2010.5462131

Cited by 136 publications

(107 citation statements)

References 28 publications

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“…The adequacy of the hyperbolic spaces for embedding of various data is also studied and confirmed in the contexts of network embedding for path cost estimation [12] and routing [13], [14], [15], [16].…”

Section: A Target Spacementioning

confidence: 89%

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Multidimensional Scaling in the Poincare disk

Cvetkovski¹,

Crovella²

2016

Appl. Math. Inf. Sci.

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Abstract-Multidimensional scaling (MDS) is a class of projective algorithms traditionally used in Euclidean space to produce two-or three-dimensional visualizations of datasets of multidimensional points or point distances.More recently however, several authors have pointed out that for certain datasets, hyperbolic target space may provide a better fit than Euclidean space. In this paper we develop PD-MDS, a metric MDS algorithm designed specifically for the Poincaré disk (PD) model of the hyperbolic plane. Emphasizing the importance of proceeding from first principles in spite of the availability of various black box optimizers, our construction is based on an elementary hyperbolic line search and reveals numerous particulars that need to be carefully addressed when implementing this as well as more sophisticated iterative optimization methods in a hyperbolic space model.

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Section: A Target Spacementioning

confidence: 89%

“…From the obtained result, symbolic derivatives of (17)- (19), as well as any other special cases derivable from (16) can be obtained by substituting appropriate constants.…”

Section: A Objective Functions and Gradientsmentioning

confidence: 99%

Multidimensional Scaling in the Poincare disk

Cvetkovski¹,

Crovella²

2016

Appl. Math. Inf. Sci.

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“…[4,32,23,24,6]). However, they do not explain why connection preferences in real networks are around the critical value and how navigable networks naturally emerge.…”

Section: Additional Related Workmentioning

confidence: 99%

A Game Theoretic Model for the Formation of Navigable Small-World Networks

Yang

Chen

2015

Proceedings of the 24th International Conference on World Wide Web

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Kleinberg proposed a family of small-world networks to explain the navigability of large-scale real-world social networks. However, the underlying mechanism that drives real networks to be navigable is not yet well understood. In this paper, we present a game theoretic model for the formation of navigable small world networks. We model the network formation as a game in which people seek for both high reciprocity and long-distance relationships. We show that the navigable small-world network is a Nash Equilibrium of the game. Moreover, we prove that the navigable small-world equilibrium tolerates collusions of any size and arbitrary deviations of a large random set of nodes, while non-navigable equilibria do not tolerate small group collusions or random perturbations. Our empirical evaluation further demonstrates that the system always converges to the navigable network even when limited or no information about other players' strategies is available. Our theoretical and empirical analyses provide important new insight on the connection between distance, reciprocity and navigability in social networks.

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“…Internet topologies have been shown to follow hyperbolic geometries [6], and several approaches have been proposed in order to optimally estimate and characterize the resulting geometric space. Robert Kleinberg proposed a simple spanning tree-based mechanism to embed I nodes of any topology into a hyperbolic geometry, which leads to low stretch in scale free graphs when combined with a local greedy forwarding policy (i.e.…”

Section: Architecture and Designmentioning

confidence: 99%

Towards Content-Centric Geometric Routing

Tavernier

Sahhaf

Colle

et al. 2014

2014 IEEE 21st Symposium on Communications and Vehicular Technology in the Benelux (SCVT)

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Abstract-Content delivery is a crucial feature of existing cloud and telecom networks. This is confirmed by the tremendous success of media streaming services such as Spotify and Netftix, as well as the content and file-distribution systems such as BitTorrent. A recurring problem in these type of network services is about keeping the protocol overhead as low as possible while maximizing the efficiency of such systems in terms of network delay to customers.In this paper we propose the use of a routing system-inferred coordinate system to improve: i) content server selection upon receiving content requests, and ii) the mapping of content to servers/caches. We describe the required protocol mechanisms, and evaluate potential gains using coordinates of Geometric Tree Routing and compare it to pure IP-based mechanisms or measurement-based content systems relying on coordinates. The proposed approach can be further extended in order to include alternate geometric systems for example supporting hyperbolic geometries.

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Greedy Forwarding in Dynamic Scale-Free Networks Embedded in Hyperbolic Metric Spaces

Cited by 136 publications

References 28 publications

Multidimensional Scaling in the Poincare disk

Multidimensional Scaling in the Poincare disk

A Game Theoretic Model for the Formation of Navigable Small-World Networks

Towards Content-Centric Geometric Routing

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