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

Fragkiskos Papadopoulos, Dmitri Krioukov, Marian Boguna, Amin Vahdat
2010 2010 Proceedings IEEE INFOCOM  
We show that complex (scale-free) network topologies naturally emerge from hyperbolic metric spaces. Hyperbolic geometry facilitates maximally efficient greedy forwarding in these networks.  ...  This remarkable efficiency sustains even in highly dynamic networks.  ...  Visualization of a modeled network embedded in the hyperbolic plane, and greedy forwarding in it.  ... 
doi:10.1109/infcom.2010.5462131 dblp:conf/infocom/PapadopoulosKBV10 fatcat:dym77j35a5e75kv4f7wawnxq4a

Greedy forwarding in scale-free networks embedded in hyperbolic metric spaces

Dmitri Krioukov, Fragkiskos Papadopoulos, Marián Boguñá, Amin Vahdat
2009 Performance Evaluation Review  
mapping of nodes to spaces of negative curvature naturally leads to the emergence of scale-free topologies; and iii) greedy routing on this embedding is efficient for these topologies, achieving both 100%  ...  The critical important question left by this work is whether the topologies of real networks can be mapped into appropriate hidden hyperbolic metric spaces.  ...  MODELS OF NETWORKS EMBEDDED IN HYPERBOLIC SPACES In this section we develop network models with nodes residing in hyperbolic spaces.  ... 
doi:10.1145/1639562.1639568 fatcat:tzg36il7srb53l4wieuct4tnca

Efficient Geometric Routing in Large-Scale Complex Networks with Low-Cost Node Design

2016 IEICE transactions on communications  
These attractive properties make the scheme promising for routing in large networks. key words: geometric routing, greedy forwarding, greedy embedding, spanning tree, large-scale topology, scale-free networks  ...  The approach guarantees that greedy forwarding on derived coordinates will result in successful packet delivery to every destination in the network by relying on coordinates deduced from a spanning tree  ...  There are several works which propose greedy embeddings in different metric spaces. Works such as [8] and [9] proposed embeddings in hyperbolic space.  ... 
doi:10.1587/transcom.2015ebp3268 fatcat:fkezzixo5fgepdclhl5wsnmyya

FPC: A self-organized greedy routing in scale-free networks

Yonggong Wang, Gaogang Xie, Mohamed-Ali Kaafar
2012 2012 IEEE Symposium on Computers and Communications (ISCC)  
In this paper we propose FPC -a Force-based layout and Path Compressing routing schema for scale-free network.  ...  As opposed to previous work, our algorithm employs a quasi-greedy but self-organized and configuration-free embedding method -force-based layout.  ...  In [6] , a strictly greedy embedding algorithm is proposed such that any connected finite graph can be embedded in two-dimension hyperbolic metric space.  ... 
doi:10.1109/iscc.2012.6249275 dblp:conf/iscc/WangXK12 fatcat:wngg6xrreje6rkv6h2ms5kipqu

Sustaining the Internet with hyperbolic mapping

Marián Boguñá, Fragkiskos Papadopoulos, Dmitri Krioukov
2010 Nature Communications  
Here we present a method to map the Internet to a hyperbolic space.  ...  Besides this immediate practical viability, our network mapping method can provide a different perspective on the community structure in complex networks.  ...  Somewhat unexpectedly, the greedy stretch is asymptotically optimal, that is, equal to 1, in scale-free, strongly clustered networks, regardless of what underlying space is used for greedy forwarding  ... 
doi:10.1038/ncomms1063 pmid:20842196 fatcat:glq4iga2hzck5alpnhsbdrhvzm

Multiscale unfolding of real networks by geometric renormalization

Guillermo García-Pérez, Marián Boguñá, M. Ángeles Serrano
2018 Nature Physics  
We find that real networks embedded in a hidden metric space show geometric scaling, in agreement with the renormalizability of the underlying geometric model.  ...  replicas of large networks and a multiscale navigation protocol in hyperbolic space which boosts the success of single-layer versions.  ...  We define a geometric renormalization group for networks by embedding them into an underlying hidden metric space.  ... 
doi:10.1038/s41567-018-0072-5 fatcat:52eqb44nnvfkvohdi4jzh5pewa

LMD: A local minimum driven and self-organized method to obtain locators

Yonggong Wang, Gaogang Xie, Mohamed-Ali Kaafar, Steve Uhlig
2013 2013 IEEE Symposium on Computers and Communications (ISCC)  
Greedy routing, in which each node is assigned a locator used as a distance metric, recently received increased attention from researchers and is considered as a potential solution for scalable routing  ...  As opposed to previous work, our algorithm employs a quasigreedy and self-organized embedding method, which outperforms similar decentralized algorithms by up to 20% in success rate.  ...  In [15] , a strictly greedy embedding algorithm is proposed such that any connected finite graph can be embedded in a twodimension hyperbolic metric space.  ... 
doi:10.1109/iscc.2013.6755040 dblp:conf/iscc/WangXKU13 fatcat:pxyyic6jrfb55lynvn7wikypfq

Dynamic greedy routing in overlay networks using virtual coordinates from the hyperbolic plane

Damien Magoni, Cyril Cassagnes
2015 Transactions on Emerging Telecommunications Technologies  
To cope with network dynamics, we have defined two methods for avoiding temporary local minima and one method for maintaining the greedy embedding over time.  ...  However, their scalability and reliability are yet to be ensured when applied to large scale dynamic networks.  ...  Other work on greedy embedding in the hyperbolic space followed in 2010 such those by Papadopoulos et al. who studied their use in dynamic scale-free networks [18] and by Zeng et al. who investigated  ... 
doi:10.1002/ett.2987 fatcat:4iw6b2k34nfy3cck7j46sso6je

Hyperbolic Embedding and Routing for Dynamic Graphs

A. Cvetkovski, M. Crovella
2009 IEEE INFOCOM 2009 - The 28th Conference on Computer Communications  
We present 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 distance routing  ...  The GP routing algorithm is applicable to networks embedded in any metric space.  ... 
doi:10.1109/infcom.2009.5062083 dblp:conf/infocom/CvetkovskiC09 fatcat:bruh3gsnrfcntaooquas7vtbka

GPS-Free Greedy Routing With Delivery Guarantee and Low Stretch Factor on 2-D and 3-D Surfaces

Su Xia, Hongyi Wu, Miao Jin
2014 IEEE Internet of Things Journal  
This paper focuses on greedy routing in wireless networks deployed on 2D and 3D surfaces. It introduces a distributed embedding scheme based on the conformal map theory.  ...  Our simulations show that its stretch factor is lower than any existing greedy embedding algorithms.  ...  Due to distortions, however, the greedy routing path in the embedded space can noticeably deviate from its counterpart in the original space and consequently the true shortest path.  ... 
doi:10.1109/jiot.2014.2320260 fatcat:ra6tehmn5fc3pm3zhixxoojqt4

Routing at Large Scale: Advances and Challenges for Complex Networks

Sahel Sahhaf, Wouter Tavernier, Dimitri Papadimitriou, Davide Careglio, Alok Kumar, Christian Glacet, David Coudert, Nicolas Nisse, Lluis Fabrega, Pere Vila, Miguel Camelo, Pieter Audenaert (+2 others)
2017 IEEE Network  
Scale-free networks are one of the well known classes of complex networks in which nodes' degrees follow a power-law distribution.  ...  improve scalability in terms of memory space.  ...  Figure 4a depicts the greedy embedding and greedy forwarding in GTR.  ... 
doi:10.1109/mnet.2017.1600203 fatcat:h7xdg4j665cvthegv3eptkxrli

Navigability of temporal networks in hyperbolic space

Elisenda Ortiz, Michele Starnini, M. Ángeles Serrano
2017 Scientific Reports  
Here, we analyze the navigability of real networks by using greedy routing in hyperbolic space, where the nodes are subject to a stochastic activation-inactivation dynamics.  ...  Maps produced by embedding the networks in hyperbolic space can assist this task enabling the implementation of efficient navigation strategies.  ...  McDonnell Foundation Scholar Award in Complex Systems, the Ministerio de Economía y Competitividad of Spain projects no. FIS2013-47282-C2-1-P and no.  ... 
doi:10.1038/s41598-017-15041-0 pmid:29118421 pmcid:PMC5678097 fatcat:kg6askytcbgxpeglvdcpl2xt54

Navigation in Real-World Complex Networks through Embedding in Latent Spaces [chapter]

Xiaomeng Ban, Jie Gao, Arnout van de Rijt
2010 2010 Proceedings of the Twelfth Workshop on Algorithm Engineering and Experiments (ALENEX)  
In this paper we apply algorithmic methods to embed nodes in some latent space and employ greedy routing to deliver packages.  ...  Small-world experiments in which packages reach addressees unknown to the original sender through a forwarding chain confirm that acquaintance networks have short paths, a property that was later also  ...  We acknowledge Lada Adamic for sharing with us the Gnutella network data set generated by Clip2. We thank Steve Skiena and Charles Ward for sharing with us the New York Times data. X. Ban and J.  ... 
doi:10.1137/1.9781611972900.13 dblp:conf/alenex/BanGR10 fatcat:s76ytlbog5gobhpo4lf446nas4

Self-organized emergence of navigability on small-world networks

Zhao Zhuo, Shi-Min Cai, Zhong-Qian Fu, Wen-Xu Wang
2011 New Journal of Physics  
Navigation based on distances between vertices in the hidden metric space can efficiently deliver messages on small-world networks, in which long range connections play an important role.  ...  Through a process of information exchange and accumulation on networks, a hidden metric space for navigation on networks is constructed.  ...  Boguñá et al have generated Internet-like scale-free networks with high navigability by embedding vertices into hyperbolic metric space and adding links between nearby vertices according to probability  ... 
doi:10.1088/1367-2630/13/5/053030 fatcat:ehqxniejmfgibglrhrgvkfaz6u

Navigability of temporal networks in hyperbolic space [article]

Elisenda Ortiz, Michele Starnini, M.Ángeles Serrano
2017 arXiv   pre-print
Here, we analyze the navigability of real networks by using greedy routing in hyperbolic space, where the nodes are subject to a stochastic activation-inactivation dynamics.  ...  Maps produced by embedding the networks in hyperbolic space can assist this task enabling the implementation of efficient navigation strategies.  ...  Hyperbolic maps In the hyperbolic hidden metric space, every node i has coordinates (r i ,θ i ). Embedding a network in a metric space means constructing a map that correlates topology and geometry.  ... 
arXiv:1709.02623v1 fatcat:yzlwkhsukrc5xij4pbwssa4tw4
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