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Edge-Packings of Graphs and Network Reliability
[chapter]

1988
*
Annals of Discrete Mathematics
*

The

doi:10.1016/s0167-5060(08)70770-2
fatcat:gejugmxtiffv5i6ac5bosrjr5i
*reliability**of*a*network*can be efficiently bounded using*graph*-theoretical techniques based on*edge*-*packing*. ...*Edge*-*packings**of**graphs*An*edge*-*packing**of*a multigraph G is a collection*of**edge*-disjoint subgraphs*of*G. ... Acknowledgements Thanks to University*of*Auckland*and*University*of*Toronto for hospitality while this paper was written,*and*to NSERC Canada for financial support. ...##
###
Edge-packing of graphs and network reliability

1988
*
Discrete Mathematics
*

The

doi:10.1016/0012-365x(88)90193-8
fatcat:lx7uhfhnx5bfnoolloblbbyhwm
*reliability**of*a*network*can be efficiently bounded using*graph*-theoretical techniques based on*edge*-*packing*. ...*Edge*-*packings**of**graphs*An*edge*-*packing**of*a multigraph G is a collection*of**edge*-disjoint subgraphs*of*G. ... Acknowledgements Thanks to University*of*Auckland*and*University*of*Toronto for hospitality while this paper was written,*and*to NSERC Canada for financial support. ...##
###
Page 3397 of Mathematical Reviews Vol. , Issue 88g
[page]

1988
*
Mathematical Reviews
*

The paper deals with probabilistic

*graphs*concerning communica- tion*network**reliability*. ... Let G*and*B be simple*graphs**and*let g be a function from V (G) onto V (B). Suppose that, for every*edge*uv*of*B, the set*of**edges**of*...##
###
The Delta-Wye Approximation Procedure for Two-Terminal Reliability

1996
*
Operations Research
*

The Delta-Wye Approximation Procedure (DWAP) is a procedure for estimating the two-terminal

doi:10.1287/opre.44.5.745
fatcat:2cux534wifgabhtsfsnuwghyqi
*reliability**of*an undirected planar*network*G = (V; E) by reducing the*network*to a single*edge*via a sequence ...*of*local*graph*transformations. ... Comparison*of*delta-wye*and**edge*-*packing*bounds for example*graphs*grid # nodes #*edges*# transf. Comparison*of*delta-wye*and*lattice bounds for grid*graphs*Table 3. ...##
###
When trees collide

1991
*
Proceedings of the twenty-third annual ACM symposium on Theory of computing - STOC '91
*

An instance consists

doi:10.1145/103418.103437
dblp:conf/stoc/AgrawalKR91
fatcat:je4bopd2vfbkpcbivmjinad7oy
*of*a*network*with link-costs*and*} for each pair {i, j}*of*nodes, an*edge*-connectivity requirement Tij. ... As a consequence*of*the proof*of*this theorem, we obtain an approximation algorithm for optimally*packing*these cuts; we show that this algorithm has application to estimating the*reliability**of*a probabilistic ... Acknowledgements Thanks to Marshall Berne, Michel*and*Richard Wong. ...##
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When Trees Collide: An Approximation Algorithm for the Generalized Steiner Problem on Networks

1995
*
SIAM journal on computing (Print)
*

An instance consists

doi:10.1137/s0097539792236237
fatcat:hmehrhjj6nfjlnvj35ypnh3hde
*of*a*network*with link-costs*and*} for each pair {i, j}*of*nodes, an*edge*-connectivity requirement Tij. ... As a consequence*of*the proof*of*this theorem, we obtain an approximation algorithm for optimally*packing*these cuts; we show that this algorithm has application to estimating the*reliability**of*a probabilistic ... Acknowledgements Thanks to Marshall Berne, Michel*and*Richard Wong. ...##
###
P3 Packing Preclusion for Hexagonal Mesh Pyramid

2014
*
International Journal of Computing Algorithm
*

Let G be a

doi:10.20894/ijcoa.101.003.002.005
fatcat:cpa5uwo2xbcl3kzoj27rurxioy
*graph*having P 3*packing*. A P 3*packing*preclusion number*of*the*graph*G is a set*of*minimum number*of**edges*, whose deletion leaves the resulting*graph*without a P 3*packing*. ... A vertex with address (k,(x,y,z)) placed at level k,*of*HX n*network*is connected to all its adjacent vertices. ... A P 3*packing*preclusion number*of*the*graph*G is a set*of*minimum number*of**edges*, whose deletion leaves the resulting*graph*without a P 3*packing*. ...##
###
Page 5941 of Mathematical Reviews Vol. , Issue 89K
[page]

1989
*
Mathematical Reviews
*

(NZ-AUCK-C)

*Edge*-*packings**of**graphs**and**network**reliability*. Proceedings*of*the First Japan Conference on*Graph*Theory*and*Applications (Hakone, 1986). Discrete Math. 72 (1988), no. 1-3, 49-61. ... The applicability*of**edge*-*packings*when deriving*reliability*bounds*of**networks*is discussed.*Edges**of*a*network*G = (V,E) operate independently with stated probabilities. ...##
###
Network design game with both reliability and security failures

2011
*
2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton)
*

We model the defender's

doi:10.1109/allerton.2011.6120233
dblp:conf/allerton/SchwartzAGW11
fatcat:v6a47qaby5a7borri426zjnfaa
*network*as an undirected*graph*with insecure*and*unreliable*edges*. ... This paper investigates the connection between*network**reliability**and*security by modeling attacker-defender interactions as a game. ... The defender's decision variable is a spanning tree*of*his*graph*,*and*the attacker's decision variable is an*edge**of*the*graph*. ...##
###
Multiplicative improvements in network reliability bounds

1989
*
Networks
*

The

doi:10.1002/net.3230190504
fatcat:3qikpsxd45f2dazarn7wjcxbbu
*network*is modelled as a probabilistic*graph*G = (V,E), in which V is a set*of*nodes representing sites in the*network*,*and*E is a collection*of*undirected*edges*representing bidirectional point-topoint ... An all-terminal operation requires that every pair*of*nodes has a path*of*operational*edges*connecting them,*and*all-terminal*reliability*is the probability that such an event occurs in the*network*. ... The second major strategy, pioneered by Polesskii [9] , employs*edge*-*packings**of**graphs*(see [2, 6] ). In this approach, one partitions the*edges**of*the*network*into subnetworks. ...##
###
Page 6823 of Mathematical Reviews Vol. , Issue 91M
[page]

1991
*
Mathematical Reviews
*

Summary: “A well-known model for

*network**reliability*studies consists*of*an undirected*graph*with perfectly*reliable*nodes*and*equal*and*independent*edge*failure probabilities. ... The*network*model used here is an undirected*graph*G(V, E) with un-*reliable*vertices*and*perfect*edges*whose K-terminal*reliability*is considered. ...##
###
Page 4150 of Mathematical Reviews Vol. , Issue 92h
[page]

1992
*
Mathematical Reviews
*

Summary: “The two-terminal

*reliability**of*a*network*is the prob- ability that a specified source node*and*target node are connected by a path*of*operating*edges*. ... [Nel, Louis Daniel”] (3-CARL-C); Zhang, Fan (3-CARL) Selecting s, t-cutsets for*edge*-*packing*-based*reliability*bounds. ...##
###
Reliable assignments of processors to tasks and factoring on matroids

1993
*
Discrete Mathematics
*

Colbourn C.J.

doi:10.1016/0012-365x(93)90360-6
fatcat:envkqcy3uras7cmomv5lstbwnu
*and*ES. Elmallah,*Reliable*assignments*of*processors to tasks*and*factoring on matroids, Discrete Mathematics 114 (1993) 115-129. ... tasks,*and*a relation between the processors*and*tasks; this relation indicates the ability*of*the processor to perform the task. ...*Reliable*as.Cgnments*of*processors to tasks ,factoring on matroid.~ ...##
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Disordered contact networks in jammed packings of frictionless disks

2016
*
Journal of Statistical Mechanics: Theory and Experiment
*

We analyse properties

doi:10.1088/1742-5468/2016/11/114002
fatcat:kfsvo7eoyzgp7ji4w74uztd2na
*of*contact*networks*formed in*packings**of*soft frictionless disks near the unjamming transition. ... We construct bounds on the number*of*polygons*and*triangulation vectors that appear in such*packings*. ... Bertrand*and*Q. Wu for providing configurations that were used in the initial analysis*of*this work. We acknowledge helpful discussions with D. Dhar. K. R. acknowledges helpful discussions with A. ...##
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Reliable, Effective and Fault-Tolerant Design of Leafy Cube Interconnection Network Topology

2019
*
VOLUME-8 ISSUE-10, AUGUST 2019, REGULAR ISSUE
*

The paper attempts to evaluate the cost effectiveness,

doi:10.35940/ijitee.l2707.1081219
fatcat:rdbhx2qidve25m2gxs6e6oaizi
*reliability**and*fault tolerance aspects*of*LC interconnection*network*in order to justify the novelty in the design*of*the proposed structure. ... The various performance parameters*of*the LC*network*are studied*and*compared with the existing HC*and*its variants. ... The fault tolerance*and**packing*density along with other parameters*of*star*graphs*are extensively studied. ...
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