Large fault-tolerant interconnection networks

This paper deals with reliability and fault-tolerant properties of networks. We first survey general reliability properties of networks, in particular those concerning diameter vulnerability. Then we study in details reliability properties of some families of networks in particular de Bruijn and Kautz networks and their generalizations which appear as very good fault-tolerant networks.

[1]  Jan van Leeuwen,et al.  Diameter increase caused by edge deletion , 1987, J. Graph Theory.

[2]  Denise Amar.  On the Connectivity of Some Telecommunications Networks , 1983, IEEE Transactions on Computers.

[3]  Alan S. Wagner.  Embedding Arbitrary Binary Trees in a Hypercube , 1989, J. Parallel Distributed Comput..

[4]  Paul Feldman.  Fault tolerance of minimal path routings in a network , 1985, STOC '85.

[5]  Arunabha Sen,et al.  On an Optimally Fault-Tolerant Multiprocessor Network Architecture , 1987, IEEE Transactions on Computers.

[6]  Yehoshua Perl,et al.  Heuristics for finding a maximum number of disjoint bounded paths , 1984, Networks.

[7]  Jhing-Fa Wang,et al.  Reliable circulant networks with minimum transmission delay , 1985 .

[8]  Claudine Peyrat.  Diameter vulnerability of graphs , 1984, Discret. Appl. Math..

[9]  S. Louis Hakimi,et al.  Fault-Tolerant Routing in DeBruijn Comrnunication Networks , 1985, IEEE Transactions on Computers.

[10]  Roger C. Entringer,et al.  Geodetic connectivity of graphs , 1977 .

[11]  Dhiraj K. Pradhan.  On a Class of Fault-Tolerant Multiprocessor Network Architectures , 1982, ICDCS.

[12]  L. Lovász,et al.  Mengerian theorems for paths of bounded length , 1978 .

[13]  José Gómez Martí.  Diámetro y vulnerabilidad en redes de interconexión , 1987 .

[14]  Franco P. Preparata,et al.  The cube-connected-cycles: A versatile network for parallel computation , 1979, 20th Annual Symposium on Foundations of Computer Science (sfcs 1979).

[15]  Izhak Rubin,et al.  On diameter stability of graphs , 1978 .

[16]  de Ng Dick Bruijn.  A combinatorial problem , 1946 .

[17]  Marie-Claude Heydemann,et al.  On forwarding indices of networks , 1989, Discret. Appl. Math..

[18]  J. Bond,et al.  Diameter vulnerability in networks , 1985 .

[19]  Chak-Kuen Wong,et al.  A Combinatorial Problem Related to Multimodule Memory Organizations , 1974, JACM.

[20]  Jean-Claude Bermond,et al.  Surveys in Combinatorics: GRAPHS AND INTERCONNECTION NETWORKS: DIAMETER AND VULNERABILITY , 1983 .

[21]  Paz Morillo,et al.  On the (d, D, D, s) - Digraph Problem , 1987, AAECC.

[22]  Mateo Valero,et al.  Discrete Optimization Problem in Local Networks and Data Alignment , 1987, IEEE Transactions on Computers.

[23]  Ding-Zhu Du,et al.  Generalized de Bruijn digraphs , 1988, Networks.

[24]  Fan Chung Graham,et al.  The forwarding index of communication networks , 1987, IEEE Trans. Inf. Theory.

[25]  M. Krishnamoorthy,et al.  Fault diameter of interconnection networks , 1987 .

[26]  Gunnar E. Carlsson,et al.  Interconnection Networks Based on a Generalization of Cube-Connected Cycles , 1985, IEEE Transactions on Computers.

[27]  Miguel Angel Fiol,et al.  Line Digraph Iterations and the (d, k) Digraph Problem , 1984, IEEE Transactions on Computers.

[28]  J.-C. Bermond,et al.  An Optimization Problem in Distributed Loop Computer Networks , 1989 .

[29]  Howard J. Quaife,et al.  On (d, k, μ) Graphs , 1969, IEEE Trans. Computers.

[30]  J. W. Suurballe.  Disjoint paths in a network , 1974, Networks.

[31]  Ulrich Schumacher.  An algorithm for construction of a k-connected graph with minimum number of edges and quasiminimal diameter , 1984, Networks.

[32]  Sheldon B. Akers,et al.  On Group Graphs and Their Fault Tolerance , 1987, IEEE Transactions on Computers.

[33]  Geoffrey Exoo,et al.  A counterexample to a conjecture on paths of bounded length , 1982, J. Graph Theory.

[34]  Sudhakar M. Reddy,et al.  A Class of Graphs for Fault-Tolerant Processor Interconnections , 1984, ICDCS.

[35]  Fan Chung Graham,et al.  Diameter bounds for altered graphs , 1984, J. Graph Theory.

[36]  Danny Dolev,et al.  A New Look at Fault-Tolerant Network Routing , 1987, Inf. Comput..

[37]  Claudine Peyrat,et al.  Sufficient conditions for maximally connected dense graphs , 1987, Discret. Math..

[38]  Jean-Claude Bermond,et al.  Hamiltonian decomposition of Cayley graphs of degree 4 , 1989, J. Comb. Theory, Ser. B.

[39]  W. Mader,et al.  Minimalen-fach kantenzusammenhängende Graphen , 1971 .

[40]  Sheldon B. Akers,et al.  The Star Graph: An Attractive Alternative to the n-Cube , 1994, ICPP.

[41]  M. Watkins.  Connectivity of transitive graphs , 1970 .

[42]  Ralph Tindell,et al.  Circulants and their connectivities , 1984, J. Graph Theory.

[43]  Makoto Imase,et al.  Fault-tolerant processor interconnection networks , 1986, Systems and Computers in Japan.

[44]  Arnold L. Rosenberg,et al.  Optimal Embeddings of the FFT Graph in the Hypercube , 1988 .

[45]  Makoto Imase,et al.  Connectivity of Regular Directed Graphs with Small Diameters , 1985, IEEE Transactions on Computers.

[46]  Dhiraj K. Pradhan,et al.  Flip-Trees: Fault-Tolerant Graphs with Wide Containers , 1988, IEEE Trans. Computers.

[47]  Makoto Imase,et al.  Fault-Tolerant Routings in a kappa-Connected Network , 1988, Inf. Process. Lett..

[48]  Odile Favaron,et al.  Edge-vulnerability and mean distance , 1989, Networks.

[49]  Béla Bollobás,et al.  The Diameter of Graphs: a survey , 1981 .

[50]  W. Mader.  Über den Zusammenhang symmetrischer Graphen , 1970 .

[51]  Dhiraj K. Pradhan,et al.  Fault-tolerant computing : theory and techniques , 1986 .

[52]  Geoffrey Exoo.  On a measure of communication network vulnerability , 1982, Networks.

[53]  W. Daniel Hillis,et al.  The connection machine , 1985 .

[54]  Claudine Peyrat,et al.  Connectivity of Imase and Itoh Digraphs , 1988, IEEE Trans. Computers.

[55]  Hiroshi Nakada,et al.  Design of a d-connected digraph with a minimum number of edges and a quasiminimal diameter , 1990, Discret. Appl. Math..

[56]  Makoto Imase,et al.  A Design for Directed Graphs with Minimum Diameter , 1983, IEEE Transactions on Computers.

[57]  David Peleg,et al.  On fault tolerant routings in general networks , 1986, PODC '86.

[58]  Claude Berge,et al.  Graphs and Hypergraphs , 2021, Clustering.

[59]  Maurice Lorrain Schlumberger,et al.  De bruijn communications networks. , 1974 .

[60]  W. Mader,et al.  Surveys in Combinatorics: Connectivity and edge-connectivity in finite graphs , 1979 .

[61]  Charles Delorme,et al.  Strategies for Interconnection Networks: Some Methods from Graph Theory , 1986, J. Parallel Distributed Comput..

[62]  Pavol Hell,et al.  Counterexamples to theorems of Menger type for the diameter , 1983, Discret. Math..

[63]  Arnold L. Rosenberg,et al.  Optimal simulations of tree machines , 1986, 27th Annual Symposium on Foundations of Computer Science (sfcs 1986).

[64]  Yahya Ould Hamidoune,et al.  On the Connectivity of Cayley Digraphs , 1984, Eur. J. Comb..

[65]  Ding-Zhu Du,et al.  Doubly Linked Ring Networks , 1985, IEEE Transactions on Computers.

[66]  Alon Itai,et al.  The complexity of finding maximum disjoint paths with length constraints , 1982, Networks.

[67]  Abdol-Hossein Esfahanian,et al.  Lower-bounds on the connectivities of a graph , 1985, J. Graph Theory.

[68]  Eli Upfal,et al.  Fault Tolerance in Networks of Bounded Degree , 1988, SIAM J. Comput..

[69]  Dhiraj K. Pradhan,et al.  A Fault-Tolerant Communication Architecture for Distributed Systems , 1982, IEEE Transactions on Computers.

[70]  Andrei Z. Broder,et al.  Efficient fault tolerant routings in networks , 1984, STOC '84.

[71]  Makoto Imase,et al.  Design to Minimize Diameter on Building-Block Network , 1981, IEEE Transactions on Computers.

[72]  Eli Upfal,et al.  Fault tolerance in networks of bounded degree , 1986, STOC '86.

[73]  Jaroslav Opatrny,et al.  Highly fault-tolerant communication network models , 1989 .

[74]  Erik A. van Doorn,et al.  Connectivity of circulant digraphs , 1986, J. Graph Theory.