Explicit construction of linear sized tolerant networks
Discrete Mathematics - First Japan Conference on Graph Theory and Applications
Fast computation using faulty hypercubes
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Wildcard Dimensions, Coding Theory and Fault-Tolerant Meshes and Hypercubes
IEEE Transactions on Computers
Construction of the mesh and the torus tolerating a large number of faults
Journal of Computer and System Sciences
Fault-Tolerant Meshes with Small Degree
SIAM Journal on Computing
Efficient Self-Embedding of Butterfly Networks with Random Faults
SIAM Journal on Computing
Fault-Tolerant Meshes and Hypercubes with Minimal Numbers of Spares
IEEE Transactions on Computers
Fault tolerant data structures
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Fault-tolerant cube graphs and coding theory
IEEE Transactions on Information Theory - Part 2
Optimal fault-tolerant linear arrays
Proceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures
Reconfiguration Algorithms for Power Efficient VLSI Subarrays with Four-Port Switches
IEEE Transactions on Computers
International Journal of Network Management
Fault-tolerance and reconfiguration of circulant graphs and hypercubes
Proceedings of the 2008 Spring simulation multiconference
Applying fault-tolerant solutions of circulant graphs to multidimensional meshes
Computers & Mathematics with Applications
An FPGA-based fault-tolerant 2D systolic array for matrix multiplications
Transactions on computational science XIII
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In this paper, we study the design of fault-tolerant networks for arrays and meshes by adding redundant nodes and edges. For a target graph G (linear array or mesh in this paper), a graph G^{\prime} is called a k-fault-tolerant graph of G if when we remove any knodes from G^{\prime}, it still contains a subgraph isomorphic to G. The major quality measures for a fault-tolerant graph are the number of spare nodes it uses and the maximum degree it has. The degree is particularly important in practice as it poses constraints on the scalability of the system. In this paper, we aim at designing fault-tolerant graphs with both a small degree and a small number of spare nodes. The fault-tolerant graphs we obtain have degree O(1) for arrays and O(\log^3 k) for meshes. The number of spare nodes used are O(k\log^2 k) and O(k^2/\log k), respectively. Compared to the previous results, the number of spare nodes used in our construction has one fewer linear factor in k.