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

2000
*
Lecture Notes in Computer Science
*

Here, we consider the question: Are the expansion properties

doi:10.1007/10719839_4
fatcat:otmvhkxjkfe27cz2su4ljup3vi
*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] . ...##
###
Analysis of edge deletion processes on faulty random regular graphs

2003
*
Theoretical Computer Science
*

Here, we consider the question: Are the expansion properties

doi:10.1016/s0304-3975(02)00640-0
fatcat:4juqp3wyknbolbg7mxx2yud3ge
*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] . ...##
###
Random Regular Graphs with Edge Faults: Expansion through Cores
[chapter]

1998
*
Lecture Notes in Computer Science
*

Here we deal with expansion properties

doi:10.1007/3-540-49381-6_24
fatcat:54qcoe2gqfhktpru4ack76zdwq
*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 ...##
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Random regular graphs with edge faults: Expansion through cores

2001
*
Theoretical Computer Science
*

Here we deal with expansion properties

doi:10.1016/s0304-3975(00)00215-2
fatcat:6g7lve2n7rcqfk43l5iuvqbjoy
*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 ...##
###
Expansion properties of a random regular graph after random vertex deletions
[article]

2007
*
arXiv
*
pre-print

Starting with a

arXiv:math/0701863v1
fatcat:oelf57cegzhpplwijohr3k36lu
*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 ...##
###
Expansion properties of a random regular graph after random vertex deletions

2008
*
European journal of combinatorics (Print)
*

Starting with a

doi:10.1016/j.ejc.2007.06.021
fatcat:b2juwzmmibajxcbymtovan7274
*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 ...##
###
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,

doi:10.1016/s0304-3975(03)00124-5
fatcat:ixtkkstovvbd3l6njhzwhde2xy
*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. ...##
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Privacy-enhanced public view for social graphs

2009
*
Proceeding of the 2nd ACM workshop on Social web search and mining - SWSM '09
*

We consider the problem

doi:10.1145/1651437.1651445
dblp:conf/cikm/KimB09
fatcat:s67wbjznlvd7zbbikoi453eyli
*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*. ...##
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Asymptotic expansion of the multi-orientable random tensor model
[article]

2015
*
arXiv
*
pre-print

The associated tensor

arXiv:1408.5725v2
fatcat:27nbjhsoprfedbdvykechjusjq
*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. ...##
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Distributed Line Graphs: A Universal Technique for Designing DHTs Based on Arbitrary Regular Graphs

2012
*
IEEE Transactions on Knowledge and Data Engineering
*

In this paper we propose the "distributed line

doi:10.1109/tkde.2011.258
fatcat:mde7fpn665fltipk235s5cnosm
*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*. ...##
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Asymptotic Expansion of the Multi-Orientable Random Tensor Model

2015
*
Electronic Journal of Combinatorics
*

The associated tensor

doi:10.37236/4629
fatcat:vurcibyc55erfoladmzixivnce
*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. ...##
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A New Diagnosis Algorithm for Regular Interconnected Structures
[chapter]

2003
*
Lecture Notes in Computer Science
*

The correctness and completeness

doi:10.1007/978-3-540-45214-0_20
fatcat:wzsiulcgwzcqdpmyr4bz2wac74
*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. ...##
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Think globally, act locally

2013
*
Proceedings of the 12th international conference on Information processing in sensor networks - IPSN '13
*

) and the network's Laplacian (which captures the topology

doi:10.1145/2461381.2461414
dblp:conf/ipsn/LoukasZWCL13
fatcat:emmoczwhibhudpuhicvwv4zjoe
*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. ...##
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Improved Dynamic Graph Learning through Fault-Tolerant Sparsification

2019
*
International Conference on Machine Learning
*

In particular, we give theoretical

dblp:conf/icml/ZhuSLHB19
fatcat:dfazlo5zhjf4vouy7az3qzsh2e
*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. ...
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