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Analysis of edge deletion processes on faulty random regular graphs

2003
*
Theoretical Computer Science
*

Here, we consider the question: Are the expansion

doi:10.1016/s0304-3975(02)00640-0
fatcat:4juqp3wyknbolbg7mxx2yud3ge
*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. ... Following the literature we look at*random**edge**faults*of*random**regular**graphs*. ...##
###
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

doi:10.1007/10719839_4
fatcat:otmvhkxjkfe27cz2su4ljup3vi
*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. ... Following the literature we look at*random**edge**faults*of*random**regular**graphs*. ...##
###
The giant component threshold for random regular graphs with edge faults
[chapter]

1997
*
Lecture Notes in Computer Science
*

*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. ... Let G be a given

*graph*(modelling a communication network) which we assume su ers from static

*edge*

*faults*: That is we let each

*edge*of G be present independently

*with*probability p (or absent

*with*

*fault*... Moreover, this subnetwork may su er from

*edge*or node

*faults*. Our work addresses robustness

*properties*

*in*case the subnetwork is a

*random*

*regular*

*graph*su ering from

*edge*

*faults*. ...

##
###
The giant component threshold for random regular graphs with edge faults H. Prodinger

2001
*
Theoretical Computer Science
*

*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. ... Let G be a given

*graph*(modelling a communication network) which we assume su ers from static

*edge*

*faults*: That is we let each

*edge*of G be present independently

*with*probability p (or absent

*with*

*fault*... Moreover, this subnetwork may su er from

*edge*or node

*faults*. Our work addresses robustness

*properties*

*in*case the subnetwork is a

*random*

*regular*

*graph*su ering from

*edge*

*faults*. ...

##
###
Universality, Tolerance, Chaos and Order
[chapter]

2010
*
Bolyai Society Mathematical Studies
*

What is the minimum possible number of

doi:10.1007/978-3-642-14444-8_1
fatcat:qudtsgymgvaxnbjkuhybjgbtgy
*edges**in*a*graph*that contains a copy of every*graph*on n vertices*with*maximum degree a most k ? ...*In*this short survey we describe the known results focusing on the main ideas*in*the proofs, discuss the remaining open problems, and mention a recent application*in*the investigation of the complexity ...*Random*universal*fault*tolerant*graphs*It is not surprising that*random**graphs**with*appropriate number of vertices and*edge*-density are H(k, n)-universal*with*high probability. ...##
###
Random Regular Graphs with Edge Faults: Expansion through Cores
[chapter]

1998
*
Lecture Notes in Computer Science
*

Here we deal

doi:10.1007/3-540-49381-6_24
fatcat:54qcoe2gqfhktpru4ack76zdwq
*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. ... Moreover, this subnetwork may su er from*edge*or node*faults*. Our work addresses robustness*properties**in*case the subnetwork is a*random**regular**graph*su ering from*edge**faults*. ...##
###
Random regular graphs with edge faults: Expansion through cores

2001
*
Theoretical Computer Science
*

Here we deal

doi:10.1016/s0304-3975(00)00215-2
fatcat:6g7lve2n7rcqfk43l5iuvqbjoy
*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. ... Moreover, this subnetwork may su er from*edge*or node*faults*. Our work addresses robustness*properties**in*case the subnetwork is a*random**regular**graph*su ering from*edge**faults*. ...##
###
The expansion and mixing time of skip graphs with applications

2008
*
Distributed computing
*

We prove that

doi:10.1007/s00446-008-0071-3
fatcat:lkrkf2nw7jbf7pj36qfnydzfq4
*with*high probability a skip*graph*contains a 4-*regular**expander*as a subgraph, and estimate the quality of the expansion via simulations. ... We show how the expansion*property*could be used to sample a node*in*the skip*graph**in*a highly efficient manner. ...*In*fact, we prove a much stronger result:*with*high probability, a skip*graph*contains a degree-4*regular**expander*as a subgraph; i.e., it contains a degree-4*regular*subgraph*with*expansion ratio Ω(1) ...##
###
The expansion and mixing time of skip graphs with applications

2005
*
Proceedings of the 17th annual ACM symposium on Parallelism in algorithms and architectures - SPAA'05
*

We prove that

doi:10.1145/1073970.1073989
dblp:conf/spaa/AspnesW05
fatcat:vaw3jguk35concffdfujng3kdm
*with*high probability a skip*graph*contains a 4-*regular**expander*as a subgraph, and estimate the quality of the expansion via simulations. ... We show how the expansion*property*could be used to sample a node*in*the skip*graph**in*a highly efficient manner. ...*In*fact, we prove a much stronger result:*with*high probability, a skip*graph*contains a degree-4*regular**expander*as a subgraph; i.e., it contains a degree-4*regular*subgraph*with*expansion ratio Ω(1) ...##
###
Parallel algorithms based on expander graphs for optical computing

1991
*
Applied Optics
*

We show that these interconnections would result

doi:10.1364/ao.30.000917
pmid:20582083
fatcat:j3lbktu4l5ft7oyuviirs3clba
*in*a number of efficient parallel algorithms for sorting, routing, associative memory, and*fault*-tolerance networks. ... We propose interconnecting processors using certain*graphs*called*expander**graphs*, which can provide fast communication from any group of processors to the rest of the network. ...*Random*d-*Regular**Graph*. ...##
###
Page 9265 of Mathematical Reviews Vol. , Issue 2002M
[page]

2002
*
Mathematical Reviews
*

Here we deal

*with*expansion*properties*of faulty*random**regular**graphs*and show that for fixed d > 42 and p=k/d, « > 20, a*random**regular**graph**with**fault*probability f =1-—p contains a linear-size subgraph ... have the same constant width.” 2002m:68089 68R10 05SC80 68M15 Goerdt, Andreas (D-TUCHI,; Chemnitz)*Random**regular**graphs**with**edge**faults*: expansion through cores. ...##
###
Page 7777 of Mathematical Reviews Vol. , Issue 96m
[page]

1996
*
Mathematical Reviews
*

(GR-PATR-CT; Patras)

*Expander**properties**in**random**regular**graphs**with**edge**faults*. (English summary) STACS 95 (Munich, 1995), 421-432, Lecture Notes*in*Comput. Sci., 900, Springer, Berlin, 1995. ... Summary: “Let H be an undirected*graph*. A*random**graph*of type H is obtained by selecting*edges*of H independently and*with*probability p. ...##
###
Eigenvalues and expanders

1986
*
Combinatorica
*

Here we show that a

doi:10.1007/bf02579166
fatcat:3jbj4ycbsrbtfd2ktjqa6bt45e
*regular*bipartite*graph*is an*expander*ifandonly if the second largest eigenvalue of its adjacency matrix is well separated from the first. ... It also supplies an efficient algorithm for approximating the*expanding**properties*of a*graph*. The exact determination of these*properties*is known to be coNP-complete. ... Added*in*proof: Recently, Lubotzky, Phillips, and Sarnak [34] constructed, for every fixed d=p+ 1, p prime, an infinite family of d-*regular**graphs*G*with*2(G)>=d-2fd -1. ...##
###
Improving Search Using a Fault-Tolerant Overlay in Unstructured P2P Systems

2007
*
Proceedings of the International Conference on Parallel Processing
*

However, we observed that the new topology had only achieved modest improvements

doi:10.1109/icpp.2007.48
dblp:conf/icpp/AcostaC07
fatcat:fablahvky5fhdjf3v2mxy335tu
*in*search success rates. ... Using attenuated bloom filters to route messages for exact identifier searches, we show that Makalu resolved most queries*with*less than ten messages for networks as large as 100,000 nodes. ... Although*regular**random**graphs*are theoretically good*expanders*, creating a P2P system using k-*regular**random**graph*on real networks poses several problems. ...##
###
Fault tolerant graphs, perfect hash functions and disjoint paths

1992
*
Proceedings., 33rd Annual Symposium on Foundations of Computer Science
*

Given a

doi:10.1109/sfcs.1992.267781
dblp:conf/focs/AjtaiABCHNS92
fatcat:uoytjtnbkvbkfhise2i3ofrcem
*graph*G on n nodes we say that a*graph*T on n + k nodes is a k-*fault*tolerant version of G, if we can embed G*in*any n node induced subgraph of T. ... We show that for a wide range of values of n, k and d, for any*graph*on n nodes*with*maximum degree d there is a k-*fault*tolerant*graph**with*maximum degree O(kd). ... The crucial*property*of an*expander*which is used here is the fact that some of its expansion*properties*remain even after deleting many of its*edges*. ...
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