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## Fault Tolerant Routing in the Star and Pancake Interconnection Networks (0)

Venue: | Information Processing Letters |

Citations: | 10 - 0 self |

### Citations

282 |
A group-theoretic model for symmetric interconnection networks
- Akers, Krishnamurthy
- 1989
(Show Context)
Citation Context ...s of routings. The n-star graph and the n-pancake graph were proposed in [2], [3] and have recently received much attention because of their rich structure, small diameter and symmetry property (cf., =-=[1]-=-, [12], [13], [14], [17], [18], [19]). Our results confirm the goodness of their topology. 2 Fault tolerant routing in the star graph Let \Sigma n be the set (group) of all permutations of symbols 1; ... |

182 |
The star graph: an attractive alternative to the n-cubes
- Akers, Harel, et al.
- 1987
(Show Context)
Citation Context ...prove that if P n is the n-pancake graph then D(R(P n ; ae)=F )s4, as long as jF j ! n and ae belongs to a particular class of routings. The n-star graph and the n-pancake graph were proposed in [2], =-=[3]-=- and have recently received much attention because of their rich structure, small diameter and symmetry property (cf., [1], [12], [13], [14], [17], [18], [19]). Our results confirm the goodness of the... |

34 |
Embedding Hamiltonians and hypercubes in star interconnection graphs
- Nigam, Sahni, et al.
- 1990
(Show Context)
Citation Context ...e n-star graph and the n-pancake graph were proposed in [2], [3] and have recently received much attention because of their rich structure, small diameter and symmetry property (cf., [1], [12], [13], =-=[14]-=-, [17], [18], [19]). Our results confirm the goodness of their topology. 2 Fault tolerant routing in the star graph Let \Sigma n be the set (group) of all permutations of symbols 1; 2; : : : ; n. Give... |

33 |
An efficient sorting algorithm for the star graph interconnection network
- Menn, Somani
- 1990
(Show Context)
Citation Context ...gs. The n-star graph and the n-pancake graph were proposed in [2], [3] and have recently received much attention because of their rich structure, small diameter and symmetry property (cf., [1], [12], =-=[13]-=-, [14], [17], [18], [19]). Our results confirm the goodness of their topology. 2 Fault tolerant routing in the star graph Let \Sigma n be the set (group) of all permutations of symbols 1; 2; : : : ; n... |

25 | A New Look at FaultTolerant Network Routing
- Dolev, Halpern, et al.
- 1987
(Show Context)
Citation Context ...and with an edge connecting vertices x and y iff ae(x; y) does not contain elements of F . Note that for bidirectional routing ae, R(G; ae)=F is an undirected graph. The seminal paper of Dolev et al. =-=[5]-=- initiated the study of the diameter D(R(G; ae)=F ) and started a fruitful line of research [4], [6], [7], [8],[11], [10], [16], [20], [21]. The motivations in [5] were based on the observation that i... |

24 | On Group Graphs and Their Fault Tolerance - Akers, Krishnamurthy - 1987 |

24 |
private communication
- Qiu
- 1992
(Show Context)
Citation Context ... the n-pancake graph were proposed in [2], [3] and have recently received much attention because of their rich structure, small diameter and symmetry property (cf., [1], [12], [13], [14], [17], [18], =-=[19]-=-). Our results confirm the goodness of their topology. 2 Fault tolerant routing in the star graph Let \Sigma n be the set (group) of all permutations of symbols 1; 2; : : : ; n. Given u = u 1 : : : u ... |

13 |
Akl "Decomposing a Star Graph into Disjoint Cycles
- Qiu, Meijer, et al.
- 1991
(Show Context)
Citation Context ...ar graph and the n-pancake graph were proposed in [2], [3] and have recently received much attention because of their rich structure, small diameter and symmetry property (cf., [1], [12], [13], [14], =-=[17]-=-, [18], [19]). Our results confirm the goodness of their topology. 2 Fault tolerant routing in the star graph Let \Sigma n be the set (group) of all permutations of symbols 1; 2; : : : ; n. Given u = ... |

8 |
Dhall, "Embedding of Cycles and Grids in Star Graphs
- Jwo, Lakshmivarahan, et al.
- 1991
(Show Context)
Citation Context ...routings. The n-star graph and the n-pancake graph were proposed in [2], [3] and have recently received much attention because of their rich structure, small diameter and symmetry property (cf., [1], =-=[12]-=-, [13], [14], [17], [18], [19]). Our results confirm the goodness of their topology. 2 Fault tolerant routing in the star graph Let \Sigma n be the set (group) of all permutations of symbols 1; 2; : :... |

7 |
Efficient fault tolerant routings in networks
- Broder, Fischer, et al.
- 1984
(Show Context)
Citation Context ... that for bidirectional routing ae, R(G; ae)=F is an undirected graph. The seminal paper of Dolev et al. [5] initiated the study of the diameter D(R(G; ae)=F ) and started a fruitful line of research =-=[4]-=-, [6], [7], [8],[11], [10], [16], [20], [21]. The motivations in [5] were based on the observation that in a communication network with a fixed routing, the time required to send a message along a rou... |

7 |
Fault-tolerant routing in double-loop networks, Ars Combin. 25A
- Escudero, FiUabrea, et al.
- 1998
(Show Context)
Citation Context ... for bidirectional routing ae, R(G; ae)=F is an undirected graph. The seminal paper of Dolev et al. [5] initiated the study of the diameter D(R(G; ae)=F ) and started a fruitful line of research [4], =-=[6]-=-, [7], [8],[11], [10], [16], [20], [21]. The motivations in [5] were based on the observation that in a communication network with a fixed routing, the time required to send a message along a route is... |

7 |
On Fault Tolerant Routings in General Networks
- Peleg, Simons
- 1987
(Show Context)
Citation Context ... ae, R(G; ae)=F is an undirected graph. The seminal paper of Dolev et al. [5] initiated the study of the diameter D(R(G; ae)=F ) and started a fruitful line of research [4], [6], [7], [8],[11], [10], =-=[16]-=-, [20], [21]. The motivations in [5] were based on the observation that in a communication network with a fixed routing, the time required to send a message along a route is often dominated by the mes... |

6 |
Parallel routing and sorting on the pancake network
- Qiu, Meijer, et al.
- 1991
(Show Context)
Citation Context ...ph and the n-pancake graph were proposed in [2], [3] and have recently received much attention because of their rich structure, small diameter and symmetry property (cf., [1], [12], [13], [14], [17], =-=[18]-=-, [19]). Our results confirm the goodness of their topology. 2 Fault tolerant routing in the star graph Let \Sigma n be the set (group) of all permutations of symbols 1; 2; : : : ; n. Given u = u 1 : ... |

2 |
K.Wada: \New results in graph routing
- Kawaguchi
- 1993
(Show Context)
Citation Context ...outing ae, R(G; ae)=F is an undirected graph. The seminal paper of Dolev et al. [5] initiated the study of the diameter D(R(G; ae)=F ) and started a fruitful line of research [4], [6], [7], [8],[11], =-=[10]-=-, [16], [20], [21]. The motivations in [5] were based on the observation that in a communication network with a fixed routing, the time required to send a message along a route is often dominated by t... |

2 |
Highly Fault--Tolerant Communication Network Models
- Opatrny, Srinivasan, et al.
- 1989
(Show Context)
Citation Context ...lem. One of the most interesting results given in [5] is that for any minimal length routing ae on the n-dimensional hypercube H n the diameter D(R(H n ; ae)=F ) is at most 3, as long as jF j ! n. In =-=[15]-=- a Research supported by Progetto Finalizzato Sistemi Informatici e Calcolo Parallelo of C.N.R. under grant n. 91.00939.PF69. class of graphs G based on balanced incomplete block designs is presented ... |

2 |
and K.Kawaguchi: \Optimal Fault-tolerant Routings for Connected Graphs
- Wada
- 1992
(Show Context)
Citation Context ...)=F is an undirected graph. The seminal paper of Dolev et al. [5] initiated the study of the diameter D(R(G; ae)=F ) and started a fruitful line of research [4], [6], [7], [8],[11], [10], [16], [20], =-=[21]-=-. The motivations in [5] were based on the observation that in a communication network with a fixed routing, the time required to send a message along a route is often dominated by the message process... |

1 |
Fault Tolerance of Minimal Path Routings in a Network
- Feldmann
- 1985
(Show Context)
Citation Context ...bidirectional routing ae, R(G; ae)=F is an undirected graph. The seminal paper of Dolev et al. [5] initiated the study of the diameter D(R(G; ae)=F ) and started a fruitful line of research [4], [6], =-=[7]-=-, [8],[11], [10], [16], [20], [21]. The motivations in [5] were based on the observation that in a communication network with a fixed routing, the time required to send a message along a route is ofte... |

1 |
On Surviving Route Graphs of Iterated Line Digraphs
- Fiol, F'abrega, et al.
- 1988
(Show Context)
Citation Context ...ectional routing ae, R(G; ae)=F is an undirected graph. The seminal paper of Dolev et al. [5] initiated the study of the diameter D(R(G; ae)=F ) and started a fruitful line of research [4], [6], [7], =-=[8]-=-,[11], [10], [16], [20], [21]. The motivations in [5] were based on the observation that in a communication network with a fixed routing, the time required to send a message along a route is often dom... |

1 |
Papadimitriou, "Bounds for Sorting by Prefix Reversal
- Gates, H
- 1979
(Show Context)
Citation Context ...Sigma n and edge set E(P n ) = f(u; u(i)) : u 2 \Sigma n ; 2sisng: P n is a Cayley graph, is regular of degree n \Gamma 1, is vertex symmetric and has diameter upper bounded by d5(n + 1)=3e (see [1], =-=[9]-=-). Finally, denote by\Omega the class of routings ae on P n satisfying: 1. if x; y 2 \Sigma n ; x n = y n then ae(x; y) contains only vertices u such that u n = x n ; 2. if x; y 2 \Sigma n , y = x(i) ... |

1 |
Fault--Tolerant Routings in a -Connected Network
- Imase, Manabe
- 1988
(Show Context)
Citation Context ...onal routing ae, R(G; ae)=F is an undirected graph. The seminal paper of Dolev et al. [5] initiated the study of the diameter D(R(G; ae)=F ) and started a fruitful line of research [4], [6], [7], [8],=-=[11]-=-, [10], [16], [20], [21]. The motivations in [5] were based on the observation that in a communication network with a fixed routing, the time required to send a message along a route is often dominate... |

1 |
Efficient Fault--Tolerant Fixed Routings on (k + 1)--Connected Digraphs
- Wada, Kawaguchi
(Show Context)
Citation Context ...(G; ae)=F is an undirected graph. The seminal paper of Dolev et al. [5] initiated the study of the diameter D(R(G; ae)=F ) and started a fruitful line of research [4], [6], [7], [8],[11], [10], [16], =-=[20]-=-, [21]. The motivations in [5] were based on the observation that in a communication network with a fixed routing, the time required to send a message along a route is often dominated by the message p... |