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On triangulation of simple networks

Robert Krauthgamer
2007 Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures - SPAA '07  
We provide the first lower bounds on the number of beacons required for a triangulation in some specific simple networks.  ...  a triangulation that approximates arbitrarily well all pairwise distances using only O(log n) beacons per point, where n is the number of points in the network.  ...  Acknowledgments I thank Alex Andoni and Alex Slivkins for useful discussions of certain technical specifics at different stages of the work.  ... 
doi:10.1145/1248377.1248380 dblp:conf/spaa/Krauthgamer07 fatcat:4balul4asbbxtm63mi3q3ay2ui

Random cubic planar graphs converge to the Brownian sphere [article]

Marie Albenque, Éric Fusy, Thomas Lehéricy
2022 arXiv   pre-print
Then, Whitney's theorem ensures that a 3-connected cubic planar graph is the dual of a simple triangulation, for which it is known that the scaling limit is the Brownian sphere.  ...  By extending this framework to simple triangulations, it is shown that 3-connected cubic planar graphs with modified distances converge jointly with their dual triangulation to the Brownian sphere.  ...  E.F. acknowledges the support of the ANR grant GATO (ANR-16-CE40-0009-01) and the ANR grant Combine (ANR-19-CE48-0011).  ... 
arXiv:2203.17245v2 fatcat:qu46kxkljjaytg5hayrof2nhda

Network, cluster coordinates and N = 2 theory II: Irregular singularity [article]

Dan Xie
2012 arXiv   pre-print
In particular, we conjecture that the quiver from the network is the BPS quiver. Moreover, our construction provides a simple way to build the minimal network for cells of positive Grassmannia .  ...  Cluster coordinates for a large class of Argyres-Douglas and asymptotical free theories are constructed using network on bordered Riemann surface.  ...  Department of Energy, grant DE-FG02-90ER40542 (DX).  ... 
arXiv:1207.6112v1 fatcat:lp7pzs7n2rclvmocxtqasg2qku

Page 4769 of Mathematical Reviews Vol. , Issue 98H [page]

1998 Mathematical Reviews  
One consequence of this result is that any triangulation of the Klein bottle has essential simple closed curves (made up of edges) of all three types (meridian, equator, and longitudinal). D.  ...  The number of distinct simple Venn diagrams with four curves (| on the sphere, 2 on the plane), known already to Griinbaum, is determined again.  ... 

Quantum Algorithms for Invariants of Triangulated Manifolds [article]

Gorjan Alagic, Edgar A. Bering IV
2011 arXiv   pre-print
One of the apparent advantages of quantum computers over their classical counterparts is their ability to efficiently contract tensor networks.  ...  The graph underlying these networks is given by the triangulation of a manifold, and the structure of the tensors ensures that the overall tensor is independent of the choice of internal triangulation.  ...  Acknowledgements G.A. is indebted to Alex Russell and Cris Moore for first telling us about the idea of approximating topological invariants by contracting tensor networks.  ... 
arXiv:1108.5424v1 fatcat:j7ttypzdjfeu7gdqg5tmviu5gy

Network, Cluster coordinates and N=2 theory I [article]

Dan Xie
2012 arXiv   pre-print
The construction starts with a triangulation of the punctured Riemann surface and a further tessellation of all the triangles.  ...  dimensional (2,0) theory on a punctured Riemann surface.  ...  The research of DX is support by the friends of Institute for Advanced Study and acknowledges support by the U.S. Department of Energy, grant DE-FG02-90ER40542.  ... 
arXiv:1203.4573v2 fatcat:gzkvgdrbtfebhnj4arhdbwtspa

Delaunay Triangulation Based Key Distribution for Wireless Sensor Network

Monjul Saikia, Computer Science and Engineering Department, North Eastern Regional Institute of Science and Technology, Nirjuli-791109, Arunachal Pradesh, India, Md. Anwar Hussain
2019 Journal of Communications  
Delaunay triangulation is a triangulation method which forms a set of triangles for a given set of points such that no point falls inside the Delaunay disk of any triangle.  ...  The key distribution in a wireless sensor network is a security phase, which involves distribution secret keys among sensor nodes prior to deployment.  ...  Two simple construction model of Delaunay triangulation is given by D. Lee et al. [20] . W. Schroeder et al.  ... 
doi:10.12720/jcm.14.7.530-537 fatcat:izosg2m3rnav7fnr7bicfdflcy

Optical wireless localization

Mehmet Bilgi, Abdullah Sevincer, Murat Yuksel, Nezih Pala
2011 Wireless networks  
In this paper, we explore the possibility of using directionality of free-space-optical (a.k.a. optical wireless) communications for solving the 3-D localization problem in ad-hoc networking environments  ...  We conclude that although denser deployments are desirable for higher accuracy, our method still works well with sparse networks with little message overhead and small number of anchor nodes (as little  ...  We used readily available directionality information to perform a simple triangulation.  ... 
doi:10.1007/s11276-011-0396-x fatcat:ns73qsrmcfcjtn4w6cffaypiw4

3-D Optical wireless localization

Mehmet Bilgi, Murat Yuksel, Nezih Pala
2010 2010 IEEE Globecom Workshops  
In this paper, we explore the possibility of using directionality of free-space-optical (a.k.a. optical wireless) communications for solving the 3-D localization problem in ad-hoc networking environments  ...  We conclude that although denser deployments are desirable for higher accuracy, our method still works well with sparse networks with little message overhead and small number of anchor nodes (as little  ...  We used readily available directionality information to perform a simple triangulation.  ... 
doi:10.1109/glocomw.2010.5700097 fatcat:hlz6oy7hijbqjda2kzpaq6gz4y

Tysserand - Fast reconstruction of spatial networks from bioimages [article]

Alexis Coullomb, Vera Pancaldi
2020 bioRxiv   pre-print
Motivation: Networks provide a powerful framework to analyze spatial omics experiments.  ...  It is intended as a common tool where the bioinformatics community can add new methods to reconstruct networks, choose appropriate parameters, clean resulting networks and pipe data to other libraries.  ...  Internally, tysserand adopts simple and efficient representations of networks to allow rapid prototyping of new network construction or cleaning methods.  ... 
doi:10.1101/2020.11.16.385377 fatcat:r36azedkmvey5ous2kmpveg6ca

Hitting times and resistance distances of q-triangulation graphs: Accurate results and applications [article]

Yibo Zeng, Zhongzhi Zhang
2018 arXiv   pre-print
For a simple connected graph G, its q-triangulation graph R_q(G) is obtained from G by performing the q-triangulation operation on G.  ...  In this paper, we study hitting times and resistance distances of q-triangulation graphs.  ...  In this paper, we provide an in-depth study on the properties for q-triangulation graph R q (G) of an arbitrary simple connected graph G, focusing on random walks and resistance distances, both of which  ... 
arXiv:1808.01025v1 fatcat:ajq6ef52ovefro6yox3qmn3l6i

Bounded stretch geographic homotopic routing in sensor networks

Kan Huang, Chien-Chun Ni, Rjk Sarkar, Jie Gao, Joseph S. B. Mitchell
2014 IEEE INFOCOM 2014 - IEEE Conference on Computer Communications  
Our routing scheme operates on two levels enabled by a coarse triangulation.  ...  Our main insight is that in a sequence of triangles to traverse, a message always routed to the nearest point on the next triangle in the sequence travels at most a constant times the length of any shortest  ...  stretch, since we can always triangulate each simple polygon.  ... 
doi:10.1109/infocom.2014.6848027 dblp:conf/infocom/HuangNSGM14 fatcat:2lmw32aisngxxipdpsim3ya7lm

Incremental Compilation of Bayesian networks [article]

Julia M. Flores, Jose A. Gamez, Kristian G. Olesen
2012 arXiv   pre-print
In this paper we present a method for incremental compilation of a Bayesian network, following the classical scheme in which triangulation plays the key role.  ...  The possibility of reusing an already existing JT, in order to obtain the new one regarding only the modifications in the network has received only little attention in the literature.  ...  Figure 1 : 1 Two representations of a Bayesian network. Figure 3 : 3 (a) The Asia network. (b) Moral graph for Asia. (c) Triangulated graph for Asia. (d) A join tree for Asia.  ... 
arXiv:1212.2456v1 fatcat:h2ddei7bv5bzzh5dgclhuojed4

Random and frozen states in complex triangulations

Tomaso Aste, Ruggero Gramatica, T. Di Matteo
2012 Philosophical Magazine  
One of the simplest and most common network is the soap froth that can form fascinating patterns and, when squeezed between two plates, reveals a very simple graph-structure with regular minimal degree  ...  Let us stress that any network can be made from the pruning of a triangulation embedded on a surface with large enough genus.  ... 
doi:10.1080/14786435.2011.613861 fatcat:agaoaqlk5najfe5nzmdgvcbvfy

Simplex triangulation induced scale-free networks [article]

Zhi-Ming Gu, Tao Zhou, Bing-Hong Wang, Gang Yan, Chen-Ping Zhu and Zhong-Qian Fu
2005 arXiv   pre-print
These networks are called simplex triangulation networks(STNs) as they can be considered as a kind of network representation of simplex triangulation.  ...  We propose a simple rule that generates scale-free networks with very large clustering coefficient and very small average distance.  ...  These networks are called simplex triangulation networks(STNs) as they can be considered as the one-dimensional framework of simplex triangulation in the view of algebraic topology [9] .  ... 
arXiv:cond-mat/0505175v1 fatcat:mgospxdrajcfhkn3getetpcxkq
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