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Analysis of Edge Deletion Processes on Faulty Random Regular Graphs [chapter]

Andreas Goerdt, Mike Molloy
2000 Lecture Notes in Computer Science  
Here, we consider the question: Are the expansion properties of random regular graphs preserved when each edge gets faulty independently of other edges with a given fault probability?  ...  Random regular graphs are, at least theoretically, popular communication networks.  ...  A faulty edge is of no use at all and thus can be considered as being deleted. The investigation of random regular graphs with edge faults starts with the paper [11] .  ... 
doi:10.1007/10719839_4 fatcat:otmvhkxjkfe27cz2su4ljup3vi

Analysis of edge deletion processes on faulty random regular graphs

Andreas Goerdt, Mike Molloy
2003 Theoretical Computer Science  
Here, we consider the question: Are the expansion properties of random regular graphs preserved when each edge gets faulty independently of other edges with a given fault probability?  ...  Random regular graphs are, at least theoretically, popular communication networks.  ...  A faulty edge is of no use at all and thus can be considered as being deleted. The investigation of random regular graphs with edge faults starts with the paper [11] .  ... 
doi:10.1016/s0304-3975(02)00640-0 fatcat:4juqp3wyknbolbg7mxx2yud3ge

Random Regular Graphs with Edge Faults: Expansion through Cores [chapter]

Andreas Goerdt
1998 Lecture Notes in Computer Science  
Here we deal with expansion properties of faulty random regular graphs and show: For ÿxed d¿42 and p = Ä=d; Ä¿20, a random regular graph with fault probability f = 1 − p contains a linear-size subgraph  ...  In particular, we are interested in robustness results for the case that the graph G itself is a random member of the class of all regular graphs with given degree d.  ...  The tight analysis of an edge deletion process similar to ours for random graphs without degree bound [18] cannot directly be transferred to the present situation because the crucial di erential equations  ... 
doi:10.1007/3-540-49381-6_24 fatcat:54qcoe2gqfhktpru4ack76zdwq

Random regular graphs with edge faults: Expansion through cores

Andreas Goerdt
2001 Theoretical Computer Science  
Here we deal with expansion properties of faulty random regular graphs and show: For ÿxed d¿42 and p = Ä=d; Ä¿20, a random regular graph with fault probability f = 1 − p contains a linear-size subgraph  ...  In particular, we are interested in robustness results for the case that the graph G itself is a random member of the class of all regular graphs with given degree d.  ...  The tight analysis of an edge deletion process similar to ours for random graphs without degree bound [18] cannot directly be transferred to the present situation because the crucial di erential equations  ... 
doi:10.1016/s0304-3975(00)00215-2 fatcat:6g7lve2n7rcqfk43l5iuvqbjoy

Expansion properties of a random regular graph after random vertex deletions [article]

Catherine Greenhill, Fred B. Holt
2007 arXiv   pre-print
Starting with a random regular graph of constant degree, delete each vertex independently with probability p, where p=n^-alpha and alpha=alpha(n) is bounded away from 0.  ...  Sharper results are obtained with extra conditions on alpha. These results have an application to the cost of repairing a certain peer-to-peer network after random failures of nodes.  ...  For random regular graphs, Pittel [12] gave a more detailed analysis and determined the order of the transition window of appearance of a giant component in a random regular graph under edge percolation  ... 
arXiv:math/0701863v1 fatcat:oelf57cegzhpplwijohr3k36lu

Expansion properties of a random regular graph after random vertex deletions

Catherine Greenhill, Fred B. Holt, Nicholas Wormald
2008 European journal of combinatorics (Print)  
Starting with a random regular graph of constant degree, delete each vertex independently with probability p, where p = n −α and α = α(n) is bounded away from 0.  ...  Sharper results are obtained with extra conditions on α. These results have an application to the cost of repairing a certain peer-to-peer network after random failures of nodes.  ...  For random regular graphs, Pittel [12] gave a more detailed analysis and determined the order of the transition window of appearance of a giant component in a random regular graph under edge percolation  ... 
doi:10.1016/j.ejc.2007.06.021 fatcat:b2juwzmmibajxcbymtovan7274

Page 4874 of Mathematical Reviews Vol. , Issue 2004f [page]

2004 Mathematical Reviews  
O.] (3-TRNT-C; Toronto, ON) Analysis of edge deletion processes on faulty random regular graphs. (English summary) Latin American theoretical informatics (Punta del Este, 2000). Theoret. Comput.  ...  The paper under review investigates the question whether the ex- pansion properties of random regular graphs are preserved when each edge fails independently of other edges with a given fault probability  ... 

Author index

2003 Theoretical Computer Science  
Molloy, Analysis of edge deletion processes on faulty random regular graphs (1-3) 241-260 Grabner, P.J., A. Knopfmacher and H.  ...  Ortiz, Decompositions for the edge colouring of reduced indifference graphs (1-3) 145-155 de Mello, C.P., see C.M.H. de Figueiredo (1-3) 145-155 Denise, A., see S.  ... 
doi:10.1016/s0304-3975(03)00124-5 fatcat:ixtkkstovvbd3l6njhzwhde2xy

Privacy-enhanced public view for social graphs

Hyoungshick Kim, Joseph Bonneau
2009 Proceeding of the 2nd ACM workshop on Social web search and mining - SWSM '09  
We consider the problem of releasing a limited public view of a sensitive graph which reveals at least k edges per node.  ...  If this public view is produced by uniform random sampling, an adversary can accurately approximate many sensitive features of the original graph, including the degree of individual nodes.  ...  Regular Subgraph Extraction The use of public listings is based on the (faulty) assumption that bounding the out-degree of a node prevents leaking d(u) for the original graph.  ... 
doi:10.1145/1651437.1651445 dblp:conf/cikm/KimB09 fatcat:s67wbjznlvd7zbbikoi453eyli

Asymptotic expansion of the multi-orientable random tensor model [article]

Eric Fusy, Adrian Tanasa
2015 arXiv   pre-print
The associated tensor graphs, or 3D maps, can be classified with respect to a particular integer or half-integer, the degree of the respective graph.  ...  Three-dimensional random tensor models are a natural generalization of the celebrated matrix models.  ...  This analysis relies on the reduction of colored graphs to some terminal forms, called schemes.  ... 
arXiv:1408.5725v2 fatcat:27nbjhsoprfedbdvykechjusjq

Distributed Line Graphs: A Universal Technique for Designing DHTs Based on Arbitrary Regular Graphs

Yiming Zhang, Ling Liu
2012 IEEE Transactions on Knowledge and Data Engineering  
In this paper we propose the "distributed line graphs" (DLG), a universal technique for designing DHTs based on arbitrary regular graphs.  ...  The effectiveness of our proposals is demonstrated through analysis, simulation and implementation.  ...  Constant-degree DHTs are usually designed based on a specific type of regular graphs, in which all nodes have the same number of edges.  ... 
doi:10.1109/tkde.2011.258 fatcat:mde7fpn665fltipk235s5cnosm

Asymptotic Expansion of the Multi-Orientable Random Tensor Model

Eric Fusy, Adrian Tanasa
2015 Electronic Journal of Combinatorics  
The associated tensor graphs, or 3D maps, can be classified with respect to a particular integer or half-integer, the degree of the respective graph.  ...  Three-dimensional random tensor models are a natural generalization of the celebrated matrix models.  ...  This analysis relies on the reduction of colored graphs to some terminal forms, called schemes.  ... 
doi:10.37236/4629 fatcat:vurcibyc55erfoladmzixivnce

A New Diagnosis Algorithm for Regular Interconnected Structures [chapter]

Antonio Caruso, Luiz Albini, Piero Maestrini
2003 Lecture Notes in Computer Science  
The correctness and completeness of NDA is studied through simulations on toroidal grids and hypercubes.  ...  The diagnosis is correct if the number of faulty units is not above a specified bound Tσ, asserted by the algorithm itself.  ...  This result is in accordance with the probabilistic analysis of general random graph presented by Scheinermann [19] and Blough et al.  ... 
doi:10.1007/978-3-540-45214-0_20 fatcat:wzsiulcgwzcqdpmyr4bz2wac74

Think globally, act locally

Andreas Loukas, Marco Zuniga, Matthias Woehrle, Marco Cattani, Koen Langendoen
2013 Proceedings of the 12th international conference on Information processing in sensor networks - IPSN '13  
) and the network's Laplacian (which captures the topology of the connectivity graph).  ...  Our analysis captures the impact of key parameters, such as node density, time-varying information, as well as of the addition (or removal) of links and nodes.  ...  Furthermore, we like to thank the anonymous reviewers and our shepherd Mingyan Liu for providing us detailed feedback on the draft version of this paper.  ... 
doi:10.1145/2461381.2461414 dblp:conf/ipsn/LoukasZWCL13 fatcat:emmoczwhibhudpuhicvwv4zjoe

Improved Dynamic Graph Learning through Fault-Tolerant Sparsification

Chun Jiang Zhu, Sabine Storandt, Kam-yiu Lam, Song Han, Jinbo Bi
2019 International Conference on Machine Learning  
In particular, we give theoretical analysis to upper bound the loss in the accuracy of the subsequent Laplacian-regularized estimation, graph SSL and SC, due to the FT sparsification.  ...  Extensive experiments have confirmed the computational efficiencies and accuracies of the proposed methods for learning on dynamic graphs.  ...  For every time point in [1, 10], a random number of at most 200 insertions/deletions of randomly selected edges were generated.  ... 
dblp:conf/icml/ZhuSLHB19 fatcat:dfazlo5zhjf4vouy7az3qzsh2e
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