Coding and information theory (2nd ed.)
Coding and information theory (2nd ed.)
Graphs & digraphs (2nd ed.)
Strategies for interconnection networks: some methods from graph theory
Journal of Parallel and Distributed Computing
On Designing and Reconfiguring k-Fault-Tolerant Tree Architectures
IEEE Transactions on Computers
IEEE Transactions on Computers
Performability modelling tools and techniques
Performance Evaluation
Performability Analysis: A New Algorithm
IEEE Transactions on Computers
Computer architecture: single and parallel systems
Computer architecture: single and parallel systems
Configuration of Locally Spared Arrays in the Presence of Multiple Fault Types
IEEE Transactions on Computers
The cube-connected cycles: a versatile network for parallel computation
Communications of the ACM
Almost Sure Diagnosis of Almost Every Good Element
IEEE Transactions on Computers
Safety Levels-An Efficient Mechanism for Achieving Reliable Broadcasting in Hypercubes
IEEE Transactions on Computers
Lee Distance and Topological Properties of k-ary n-cubes
IEEE Transactions on Computers
Extended Hypercube: A Hierarchical Interconnection Network of Hypercubes
IEEE Transactions on Parallel and Distributed Systems
IEEE Transactions on Parallel and Distributed Systems
Large Networks with Small Diameter
WG '97 Proceedings of the 23rd International Workshop on Graph-Theoretic Concepts in Computer Science
EH '99 Proceedings of the 1st NASA/DOD workshop on Evolvable Hardware
Extremal Graph Theory
A survey of comparison-based system-level diagnosis
ACM Computing Surveys (CSUR)
Research on petersen graphs and hyper-cubes connected interconnection networks
ACSAC'06 Proceedings of the 11th Asia-Pacific conference on Advances in Computer Systems Architecture
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We quantify why, as designers, we should prefer clique-based hypercubes (K-cubes) over traditional hypercubes based on cycles (C-cubes). Reaping fresh analytic results, we find that K-cubes minimize the wirecount and, simultaneously, the latency of hypercube architectures that tolerate failure of any f nodes. Refining the graph model of Hayes (1976), we pose the feasibility of configuration as a problem in multivariate optimization:What (f + 1){\hbox{-}}{\rm connected}n{\hbox{-}}{\rm vertex} graphs with fewest edges \lceil n ( f + 1) / 2\rceil minimize the maximum a) radius or b) diameter of subgraphs (i.e., quorums) induced by deleting up to f vertices? (1)We solve (1) for f that is superlogarithmic but sublinear in n and, in the process, prove: 1) the fault tolerance of K-cubes is proportionally greater than that of C-cubes; 2) quorums formed from K-cubes have a diameter that is asymptotically convergent to the Moore Bound on radius; 3) under any conditions of scaling, by contrast, C-cubes diverge from the Moore Bound. Thus, K-cubes are optimal, while C-cubes are suboptimal. Our exposition furthermore: 4) counterexamples, corrects, and generalizes a mistaken claim by Armstrong and Gray (1981) concerning binary cubes; 5) proves that K-cubes and certain of their quorums are the only graphs which can be labeled such that the edge distance between any two vertices equals the Hamming distance between their labels; and 6) extends our results to K-cube-connected cycles and edges. We illustrate and motivate our work with applications to the synthesis of multicomputer architectures for deep space missions.