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

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.  ...  Following the literature we look at random edge faults of random regular graphs.  ... 
doi:10.1007/10719839_4 fatcat:otmvhkxjkfe27cz2su4ljup3vi

The giant component threshold for random regular graphs with edge faults [chapter]

Andreas Goerdt
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.  ... 
doi:10.1007/bfb0029971 fatcat:5dmrqe6axne45gevocosuyhhrq

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

Andreas Goerdt
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.  ... 
doi:10.1016/s0304-3975(00)00015-3 fatcat:jrhcr4v4qrhs7o6obbetq3hkxi

Universality, Tolerance, Chaos and Order [chapter]

Noga Alon
2010 Bolyai Society Mathematical Studies  
What is the minimum possible number of 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.  ... 
doi:10.1007/978-3-642-14444-8_1 fatcat:qudtsgymgvaxnbjkuhybjgbtgy

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.  ...  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.  ... 
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.  ...  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.  ... 
doi:10.1016/s0304-3975(00)00215-2 fatcat:6g7lve2n7rcqfk43l5iuvqbjoy

The expansion and mixing time of skip graphs with applications

James Aspnes, Udi Wieder
2008 Distributed computing  
We prove that 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)  ... 
doi:10.1007/s00446-008-0071-3 fatcat:lkrkf2nw7jbf7pj36qfnydzfq4

The expansion and mixing time of skip graphs with applications

James Aspnes, Udi Wieder
2005 Proceedings of the 17th annual ACM symposium on Parallelism in algorithms and architectures - SPAA'05  
We prove that 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)  ... 
doi:10.1145/1073970.1073989 dblp:conf/spaa/AspnesW05 fatcat:vaw3jguk35concffdfujng3kdm

Parallel algorithms based on expander graphs for optical computing

Ramamohan Paturi, Dau-Tsuong Lu, Joseph E. Ford, Sadik C. Esener, Sing H. Lee
1991 Applied Optics  
We show that these interconnections would result 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.  ... 
doi:10.1364/ao.30.000917 pmid:20582083 fatcat:j3lbktu4l5ft7oyuviirs3clba

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

Noga Alon
1986 Combinatorica  
Here we show that a 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.  ... 
doi:10.1007/bf02579166 fatcat:3jbj4ycbsrbtfd2ktjqa6bt45e

Improving Search Using a Fault-Tolerant Overlay in Unstructured P2P Systems

William Acosta, Surendar Chandra
2007 Proceedings of the International Conference on Parallel Processing  
However, we observed that the new topology had only achieved modest improvements 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.  ... 
doi:10.1109/icpp.2007.48 dblp:conf/icpp/AcostaC07 fatcat:fablahvky5fhdjf3v2mxy335tu

Fault tolerant graphs, perfect hash functions and disjoint paths

M. Ajtai, N. Alon, J. Bruck, R. Cypher, C.T. Ho, M. Naor, E. Szemeredi
1992 Proceedings., 33rd Annual Symposium on Foundations of Computer Science  
Given a 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.  ... 
doi:10.1109/sfcs.1992.267781 dblp:conf/focs/AjtaiABCHNS92 fatcat:uoytjtnbkvbkfhise2i3ofrcem
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