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Edge-Packings of Graphs and Network Reliability [chapter]

Charles J. Colbourn
1988 Annals of Discrete Mathematics  
The 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.  ... 
doi:10.1016/s0167-5060(08)70770-2 fatcat:gejugmxtiffv5i6ac5bosrjr5i

Edge-packing of graphs and network reliability

Charles J. Colbourn
1988 Discrete Mathematics  
The 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.  ... 
doi:10.1016/0012-365x(88)90193-8 fatcat:lx7uhfhnx5bfnoolloblbbyhwm

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

Manoj K. Chari, Thomas A. Feo, J. Scott Provan
1996 Operations Research  
The Delta-Wye Approximation Procedure (DWAP) is a procedure for estimating the two-terminal 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.  ... 
doi:10.1287/opre.44.5.745 fatcat:2cux534wifgabhtsfsnuwghyqi

When trees collide

Ajit Agrawal, Philip Klein, R. Ravi
1991 Proceedings of the twenty-third annual ACM symposium on Theory of computing - STOC '91  
An instance consists 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.  ... 
doi:10.1145/103418.103437 dblp:conf/stoc/AgrawalKR91 fatcat:je4bopd2vfbkpcbivmjinad7oy

When Trees Collide: An Approximation Algorithm for the Generalized Steiner Problem on Networks

Ajit Agrawal, Philip Klein, R. Ravi
1995 SIAM journal on computing (Print)  
An instance consists 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.  ... 
doi:10.1137/s0097539792236237 fatcat:hmehrhjj6nfjlnvj35ypnh3hde

P3 Packing Preclusion for Hexagonal Mesh Pyramid

Deeni C J
2014 International Journal of Computing Algorithm  
Let G be a 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.  ... 
doi:10.20894/ijcoa.101.003.002.005 fatcat:cpa5uwo2xbcl3kzoj27rurxioy

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

Galina A. Schwartz, Saurabh Amin, Assane Gueye, Jean Walrand
2011 2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton)  
We model the defender's 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.  ... 
doi:10.1109/allerton.2011.6120233 dblp:conf/allerton/SchwartzAGW11 fatcat:v6a47qaby5a7borri426zjnfaa

Multiplicative improvements in network reliability bounds

Timothy B. Brecht, Charles J. Colbourn
1989 Networks  
The 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.  ... 
doi:10.1002/net.3230190504 fatcat:3qikpsxd45f2dazarn7wjcxbbu

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

Charles J. Colbourn, Ehab S. Elmallah
1993 Discrete Mathematics  
Colbourn C.J. 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.~  ... 
doi:10.1016/0012-365x(93)90360-6 fatcat:envkqcy3uras7cmomv5lstbwnu

Disordered contact networks in jammed packings of frictionless disks

Kabir Ramola, Bulbul Chakraborty
2016 Journal of Statistical Mechanics: Theory and Experiment  
We analyse properties 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.  ... 
doi:10.1088/1742-5468/2016/11/114002 fatcat:kfsvo7eoyzgp7ji4w74uztd2na

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, 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.  ... 
doi:10.35940/ijitee.l2707.1081219 fatcat:rdbhx2qidve25m2gxs6e6oaizi
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