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Connectivity of Random Annulus Graphs and the Geometric Block Model

Sainyam Galhotra, Arya Mazumdar, Soumyabrata Pal, Barna Saha, Michael Wagner
2019 International Workshop on Approximation Algorithms for Combinatorial Optimization  
This requires us to prove new connectivity results for vertex-random graphs or random annulus graphs which are natural generalizations of random geometric graphs.  ...  Random geometric graph (Gilbert, 1961) is a basic model of random graphs for spatial networks proposed shortly after the introduction of the Erdős-Rényi random graphs.  ...  APPROX/RANDOM 2019 53:10 Connectivity of Random Annulus Graphs and the Geometric Block Model Corollary 13.  ... 
doi:10.4230/lipics.approx-random.2019.53 dblp:conf/approx/GalhotraMPS19 fatcat:tetizrgfbrftbjyuavagtojt2a

Connectivity in Random Annulus Graphs and the Geometric Block Model [article]

Sainyam Galhotra, Arya Mazumdar, Soumyabrata Pal, Barna Saha
2020 arXiv   pre-print
Our next contribution is in using the connectivity of random annulus graphs to provide necessary and sufficient conditions for efficient recovery of communities for the geometric block model (GBM).  ...  We provide new connectivity results for vertex-random graphs or random annulus graphs which are significant generalizations of random geometric graphs.  ...  Defining a block model over a random geometric graph, the geometric block model (GBM), circumvents this since GBM naturally inherits the transitivity property of a random geometric graph.  ... 
arXiv:1804.05013v3 fatcat:krglqyny7be5havuidaudhqkfm

Communication-free Massively Distributed Graph Generation [article]

Daniel Funke, Sebastian Lamm, Ulrich Meyer, Peter Sanders, Manuel Penschuck, Christian Schulz, Darren Strash, Moritz von Looz
2019 arXiv   pre-print
In this work, we present novel generators for a variety of network models that are frequently used as benchmarks.  ...  However, engineering such algorithms is often hindered by the scarcity of publicly available datasets.  ...  Ministry of Education and Research (BMBF) and the German State Ministries for Research of Baden-Württemberg (MWK), Bayern (StMWFK) and Nordrhein-Westfalen (MIWF).  ... 
arXiv:1710.07565v3 fatcat:6lplo2xabvf3jd4xedqjrzb64e

Continuum Percolation with Unreliable and Spread-Out Connections

Massimo Franceschetti, Lorna Booth, Matthew Cook, Ronald Meester, Jehoshua Bruck
2005 Journal of statistical physics  
Our results indicate that real networks can exploit the presence of spread-out and unreliable connections to achieve connectivity more easily, provided they can maintain the average number of functioning  ...  We derive percolation results in the continuum plane that lead to what appears to be a general tendency of many stochastic network models.  ...  The resulting random graph can now effectively be viewed as a realization of a random connection model with density λ and connection function ph p (x) = g squash p .  ... 
doi:10.1007/s10955-004-8826-0 fatcat:zi2x3qnxmngntebv3qfaauj3qm

Connectivity and Centrality in Dense Random Geometric Graphs [article]

Alexander P. Kartun-Giles
2019 arXiv   pre-print
Our analysis involves a stochastic spatial network model called a random geometric graph, which we use to model a network of interconnected devices communicating wirelessly without any separate, pre-established  ...  [The remaining abstract is available in the front matter of this thesis.]  ...  probability P f c of soft random geometric graphs formed within the annulus and spherical shell geometries, quantifying how simple convex obstacles affect connectivity.  ... 
arXiv:1601.03296v5 fatcat:vhe2xazplfd43myy2u4elsjkrm

Multi-Dimensional Interval Algebra with Symmetry for Describing Block Layouts [chapter]

Ankur Lahoti, Rohit Singh, Amitabha Mukerjee
2000 Lecture Notes in Computer Science  
Inequalities Quadratic inequalities on a graphing calculator, solutions to systems of quadratic inequalities on a graphing calculator Chapter 1: The Building Blocks of Geometr y: Making and Measuring  ...  for Simulation Random-integer lists on a calculator, design and application of random-integer simulation schemes for various situations Looking Back, Review Exercises Related Topics Geometric Probability  ...  Graphs and Tables Chapter 4 The unit circle Display 4.17  ... 
doi:10.1007/3-540-40953-x_12 fatcat:gxyywcuhyffzrce3i7ovomwhuu

Phase transitions and percolation at criticality in enhanced random connection models [article]

Srikanth K. Iyer, Sanjoy Kr. Jhawar
2020 arXiv   pre-print
We study phase transition and percolation at criticality for three random graph models on the plane, viz., the homogeneous and inhomogeneous enhanced random connection models (RCM) and the Poisson stick  ...  The Poisson stick model consists of line segments of independent random lengths and orientation with the mid point of each segment located at a distinct point of P_λ.  ...  ACKNOWLEDGEMENTS: The authors are thankful to Mathew D. Penrose and Yogeshwaran D. for many useful discussions and references.  ... 
arXiv:1908.00346v3 fatcat:7mannbbivvdzfeiwbmmpzheami

Gromov Centrality: A Multi-Scale Measure of Network Centrality Using Triangle Inequality Excess [article]

Shazia'Ayn Babul, Karel Devriendt, Renaud Lambiotte
2022 arXiv   pre-print
We argue that Gromov centrality is affected by the geometric and boundary constraints of the network, and illustrate how it can help distinguish different types of nodes in random geometric graphs and  ...  Depending on the size of the neighborhood, the resulting Gromov centrality defines the importance of a node at different scales in the graph, and recovers as limits well-known concept such as the clustering  ...  KD was supported by The Alan Turing Institute under EPSRC grant EP/N510129/1. The work of RL was supported by EPSRC grants EP/V013068/1 and EP/V03474X/1.  ... 
arXiv:2205.04974v1 fatcat:xd4ksq7oxff3jkmn5prkfgvxkq

First Passage Percolation on Random Geometric Graphs and an Application to Shortest-Path Trees

C. Hirsch, D. Neuhäuser, C. Gloaguen, V. Schmidt
2015 Advances in Applied Probability  
Besides, for a wide class of stationary and isotropic random geometric graphs, our linear growth property implies a shape theorem for the Euclidean first passage model defined by such random geometric  ...  We consider Euclidean first passage percolation on a large family of connected random geometric graphs in the d-dimensional Euclidean space encompassing various well-known models from stochastic geometry  ...  location on the edge set of G Description of the model G = random geometric graph in R 2 as above G * = Palm version of G informally: shifting o to random location on the edge set of G Y λ = Cox process  ... 
doi:10.1239/aap/1435236978 fatcat:xwno776zqjbe3jp44o7jyv3d54

Bootstrap percolation in random geometric graphs [article]

Victor Falgas-Ravry, Amites Sarkar
2021 arXiv   pre-print
Following Bradonjić and Saniee, we study a model of bootstrap percolation on the Gilbert random geometric graph on the 2-dimensional torus.  ...  In this model, the expected number of vertices of the graph is n, and the expected degree of a vertex is alog n for some fixed a>1.  ...  Acknowledgements Research on this project was done while the second author visited the first author in Umeå in Spring 2018 with financial support from STINT Initiation grant IB 2017-7360, which the authors  ... 
arXiv:2110.12166v1 fatcat:ja27g6o2brek5ggj6sku7vu53m

Heat diffusion distance processes: a statistically founded method to analyze graph data sets [article]

Etienne Lasalle
2021 arXiv   pre-print
The statistical properties of empirical means of such processes are studied in the general case.  ...  Once applied to our processes, these results allow to analyze data sets of pairs of graphs.  ...  Acknowledgments I am thankful to Frédéric Chazal 1 and Pascal Massart 2 for the valuable discussions and advice on this work.  ... 
arXiv:2109.13213v2 fatcat:a7o57i2k2zadhdvdowmtgqckey

Exponential rate for the contact process extinction time [article]

Bruno Schapira, Daniel Valesin
2018 arXiv   pre-print
We consider the extinction time of the contact process on increasing sequences of finite graphs obtained from a variety of random graph models.  ...  of random interlacements, excursion sets of the Gaussian free field, random geometric graphs) as well as supercritical Galton-Watson trees grown up to finite generations.  ...  We would also like to thank Tobias Müller for helpful discussions and references on the random geometric graph.  ... 
arXiv:1806.04491v1 fatcat:6gx7flrdvbhmdp6duiu2zmt6na

Influence of user density distribution on the pairing probability in GSM cell with implemented VAMOS technology

Dragan Mitić, Aleksandar Lebl, Žarko Markov
2018 Automatika  
In this paper, we present the influence of user density distribution in the base station cell on the (un)pairing probability and on the loss caused by the lack of idle traffic resources in GSM systems,  ...  It is further presented to what extent the total loss in the system with the implementation of VAMOS technology is greater than the loss in the classic Erlang traffic model with the same traffic characteristics  ...  Acknowledgments The paper is written in the framework of projects TR 32051 and TR 32007.  ... 
doi:10.1080/00051144.2018.1502735 fatcat:og6s357cejfixklxrbl4jw6zce

Progressive Correspondence Pruning by Consensus Learning [article]

Chen Zhao, Yixiao Ge, Feng Zhu, Rui Zhao, Hongsheng Li, Mathieu Salzmann
2021 arXiv   pre-print
The selection is challenging since putative matches are typically extremely unbalanced, largely dominated by outliers, and the random distribution of such outliers further complicates the learning process  ...  We introduce a "pruning" block that lets us identify reliable candidates among the initial matches according to consensus scores estimated using local-to-global dynamic graphs.  ...  , and E l i indicates the set of directed edges that connect c i and its neighbors in V l i .  ... 
arXiv:2101.00591v2 fatcat:j7hz2vn6gnezdhauz52j374u3e

Exponential rate for the contact process extinction time

Bruno Schapira, Daniel Valesin
2021 Annales de la Faculté des Sciences de Toulouse  
We would also like to thank Tobias Müller for helpful discussions and references on the random geometric graph.  ...  Finally, we would like to thank the two anonymous referees of Annales de la Faculté des Sciences de Toulouse for their careful reading of the manuscript and helpful suggestions. Bibliography  ...  Random geometric graph The random geometric graph in R d , d 2, is the random graph whose vertex set is a Poisson point process of intensity one, and the edge set is defined with the rule that two vertices  ... 
doi:10.5802/afst.1683 fatcat:gnbgfmf7xjfb7f47xg47so6xdy
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