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On suitability of Euclidean embedding of internet hosts

Sanghwan Lee, Zhi-Li Zhang, Sambit Sahu, Debanjan Saha
2006 Proceedings of the joint international conference on Measurement and modeling of computer systems - SIGMETRICS '06/Performance '06  
Based on these insights, we propose a new hybrid model for embedding the network nodes using only a 2-dimensional Euclidean coordinate system and small error adjustment terms.  ...  We then show that the distance matrix among Internet hosts contains negative eigenvalues of large magnitude, implying that embedding the Internet hosts in a Euclidean space would incur relatively large  ...  The Euclidean coordinates of the SLAT (2D+1) are the first 2 coordinates of the Virtual Landmark 7 dimension embedding.  ... 
doi:10.1145/1140277.1140296 dblp:conf/sigmetrics/LeeZSS06 fatcat:cmuontacznecpjcmeia3hfst5a

On suitability of Euclidean embedding of internet hosts

Sanghwan Lee, Zhi-Li Zhang, Sambit Sahu, Debanjan Saha
2006 Performance Evaluation Review  
Based on these insights, we propose a new hybrid model for embedding the network nodes using only a 2-dimensional Euclidean coordinate system and small error adjustment terms.  ...  We then show that the distance matrix among Internet hosts contains negative eigenvalues of large magnitude, implying that embedding the Internet hosts in a Euclidean space would incur relatively large  ...  The Euclidean coordinates of the SLAT (2D+1) are the first 2 coordinates of the Virtual Landmark 7 dimension embedding.  ... 
doi:10.1145/1140103.1140296 fatcat:vbdnm6czqjbtta4wnlokzh6yva

On Suitability of Euclidean Embedding for Host-Based Network Coordinate Systems

Sanghwan Lee, Zhi-Li Zhang, S. Sahu, D. Saha
2010 IEEE/ACM Transactions on Networking  
Based on these insights, we propose a new hybrid model for embedding the network nodes using only a two-dimensional Euclidean coordinate system and small error adjustment terms.  ...  We then show that the distance matrix among Internet hosts contains negative eigenvalues of large magnitude, implying that embedding the Internet hosts in a Euclidean space would incur relatively large  ...  Hence in our hybrid model, each node has a -dim Euclidean coordinate, , and a (non-Euclidean) adjustment : we use to denote the total "coordinate" of node .  ... 
doi:10.1109/tnet.2009.2023322 fatcat:rsfu6s7tsbfivpl7derjkjxc54

On the internet delay space dimensionality

Bruno Abrahao, Robert Kleinberg
2008 Proceedings of the 8th ACM SIGCOMM conference on Internet measurement conference - IMC '08  
In this process, known as network embedding, each node is assigned a coordinate in a host metric space (e.g., Euclidean space) in such a way that the geometric distance between any two nodes estimates  ...  This observation shows evidence of non-negligible non-linear structures in the delay space and suggests that methods based on non-linear embeddings might better reflect the structural properties of the  ... 
doi:10.1145/1452520.1452541 dblp:conf/imc/AbrahaoK08 fatcat:w224hxyozrbz7jieybghjvxppi

On the internet delay space dimensionality

Bruno D. Abrahao, Robert D. Kleinberg
2008 Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing - PODC '08  
In this process, known as network embedding, each node is assigned a coordinate in a host metric space (e.g., Euclidean space) in such a way that the geometric distance between any two nodes estimates  ...  This observation shows evidence of non-negligible non-linear structures in the delay space and suggests that methods based on non-linear embeddings might better reflect the structural properties of the  ... 
doi:10.1145/1400751.1400810 dblp:conf/podc/AbrahaoK08 fatcat:xlztdu7a6zdt3e66kzq6qcqbru

Measurement Manipulation and Space Selection in Network Coordinates

Cristian Lumezanu, Neil Spring
2008 2008 The 28th International Conference on Distributed Computing Systems  
Internet coordinate systems have emerged as an efficient method to estimate the latency between pairs of nodes without any communication between them.  ...  We adapt the Vivaldi algorithm to use Hyperbolic space for embedding and evaluate both Euclidean and Hyperbolic Vivaldi on seven sets of real-world latencies.  ...  [10] add a localized adjustment term to Euclidean coordinates to account for the non-Euclidean effect of triangle inequality violations.  ... 
doi:10.1109/icdcs.2008.27 dblp:conf/icdcs/LumezanuS08 fatcat:y4ypk753jzbexpg2aivafxt2h4

Fundamental Effects of Clustering on the Euclidean Embedding of Internet Hosts [chapter]

Sanghwan Lee, Zhi-Li Zhang, Sambit Sahu, Debanjan Saha, Mukund Srinivasan
2007 Lecture Notes in Computer Science  
In this paper, we investigate why the Euclidean embedding shows reasonable accuracy despite the prevalence of TIVs, focusing in particular on the effect of clustering among Internet hosts.  ...  While some recent studies have revealed that triangle inequality violations (TIVs) inherent in network distances among Internet hosts fundamentally limit their accuracy, these Euclidean embedding methods  ...  Impact of Clusters on the Accuracy of Euclidean Embedding Euclidean embedding of network distances is basically an optimization problem.  ... 
doi:10.1007/978-3-540-72606-7_76 fatcat:vvwkcu6yqbhhrdvzmyv6ytowyy

Network(graph) data research in the coordinate system

Liu Hui, Lin Zhi, Waqas Ahmad
2018 Mathematical Foundations of Computing  
We then present two categories of approaches for Internet embedding in the coordinate system and the technology of graph embedding of social network.  ...  We first introduce the coordinate embedding and transforming of double-loop network with its symmetrical and regular structure.  ...  In Section 3, we present two categories of coordinate system of Internet, mapping Internet hosts to a specific position in a Euclidean space, and in Section 4, we propose graph coordinate system, which  ... 
doi:10.3934/mfc.2018001 fatcat:j5ikmkma4vg2bbwriude3k5dse

On the accuracy of embeddings for internet coordinate systems

Eng Keong Lua, Timothy Griffin, Marcelo Pias, Han Zheng, Jon Crowcroft
2005 Proceedings of the 5th ACM SIGCOMM conference on Internet measurement - IMC '05  
Internet coordinate systems embed Round-Trip-Times (RTTs) between Internet nodes into some geometric space so that unmeasured RTTs can be estimated using distance computation in that space.  ...  Evaluation of current Internet coordinate systems using our new metrics indicates that their quality is not as high as that suggested by the use of absolute relative error.  ...  Basically, Internet coordinate systems comprise of two categories of network embeddings of finite metric space into low dimensional Euclidean or non-Euclidean (e.g.  ... 
doi:10.1145/1330107.1330122 fatcat:ozsx2h7rv5hwvaha7gdvn4sxru

Systematic comparison of graph embedding methods in practical tasks [article]

Yi-Jiao Zhang, Kai-Cheng Yang, Filippo Radicchi
2021 arXiv   pre-print
We consider methods for embedding networks in the hyperbolic and Euclidean metric spaces, as well as non-metric community-based embedding methods.  ...  Our results show that some Euclidean embedding methods excel in greedy routing.  ...  The non-Euclidean embedding methods still present some challenges.  ... 
arXiv:2106.10198v1 fatcat:o2qbqww325cadkqo5jewa2oqwm

Towards network triangle inequality violation aware distributed systems

Guohui Wang, Bo Zhang, T. S. Eugene Ng
2007 Proceedings of the 7th ACM SIGCOMM conference on Internet measurement - IMC '07  
These neighbor selection mechanisms often assume the triangle inequality holds for Internet delays. However, the reality is that the triangle inequality is violated by Internet delays.  ...  This paper investigates the properties of triangle inequality violation (TIV) in Internet delays, the impacts of TIV on representative neighbor selection mechanisms, specifically Vivaldi and Meridian,  ...  [11] proposes to add a localized adjustment term (LAT) to Euclidean coordinates to account for the non-Euclidean effect.  ... 
doi:10.1145/1298306.1298331 dblp:conf/imc/WangZN07 fatcat:pxwwa73g5bek5e2oturw3aujfm

WSP: A Network Coordinate Based Web Service Positioning Framework for Response Time Prediction

Jieming Zhu, Yu Kang, Zibin Zheng, Michael R. Lyu
2012 2012 IEEE 19th International Conference on Web Services  
corresponding Euclidean distances.  ...  By combining the advantages of network coordinate based approaches and collaborative filtering based approaches, the response times between users and Web services can be accurately predicted using their  ...  Impact of the Coordinate Dimensionality Dimensionality is a key factor when embedding the Internet hosts into an Euclidean space.  ... 
doi:10.1109/icws.2012.81 dblp:conf/icws/ZhuKZL12 fatcat:hgyxw5i2m5dv5lfw4smnefrq5q

A sprinkling of hybrid-signature discrete spacetimes in real-world networks [article]

Astrid Eichhorn, Martin Pauly
2021 arXiv   pre-print
Many real-world networks are embedded into a space or spacetime. The embedding space(time) constrains the properties of these real-world networks.  ...  We find that spacetime networks which are inspired by quantum gravity and based on a hybrid signature, following the Minkowski metric at small spatial distance and the Euclidean metric at large spatial  ...  We will use a different distribution of coordinates for the Euclidean than for the Minkowski case for practical reasons.  ... 
arXiv:2107.07325v1 fatcat:tipmyo4i3radznvjbgdl5lbfmm

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

Dmitri Krioukov, Fragkiskos Papadopoulos, Marián Boguñá, Amin Vahdat
2009 Performance Evaluation Review  
beneath the observed topologies; ii) the most straightforward mapping of nodes to spaces of negative curvature naturally leads to the emergence of scale-free topologies; and iii) greedy routing on this embedding  ...  In his model, each node, in addition to being a part of the graph representing the global network topology, resides in a coordinate space-a grid embedded in the Euclidean plane.  ...  [30, 41, 51] or Vivaldi [13] , try to accurately estimate network delays between Internet hosts by embedding them into virtual coordinate spaces such that the distances between nodes in this space  ... 
doi:10.1145/1639562.1639568 fatcat:tzg36il7srb53l4wieuct4tnca

Phoenix: Towards an Accurate, Practical and Decentralized Network Coordinate System [chapter]

Yang Chen, Xiao Wang, Xiaoxiao Song, Eng Keong Lua, Cong Shi, Xiaohan Zhao, Beixing Deng, Xing Li
2009 Lecture Notes in Computer Science  
Network coordinate (NC) system allows efficient Internet distance prediction with scalable measurements. Most of the NC systems are based on embedding hosts into a low dimensional Euclidean space.  ...  However, it cannot guarantee the predicted distance non-negative and its prediction accuracy is close to the Euclidean distance based NC systems.  ...  Related Work Euclidean Distance Based Network Coordinates and Triangle Inequality Violation (TIV) Suppose there are N Internet hosts. Let S be the set of these N hosts.  ... 
doi:10.1007/978-3-642-01399-7_25 fatcat:6fyotrmqvvep5o32cpjmctrdyq
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