Survivable Networks with Bounded Delay: The Edge Failure Case
ISAAC '99 Proceedings of the 10th International Symposium on Algorithms and Computation
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STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
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Dynamic Fault-Tolerance and Metrics for Battery Powered, Failure-Prone Systems
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Discrete Applied Mathematics - Special issue: Max-algebra
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Online routing in faulty meshes with sub-linear comparative time and traffic ratio
ESA'05 Proceedings of the 13th annual European conference on Algorithms
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ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
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In this paper we study the ability of array-based networks to tolerate worst-case faults. We show that an $N \times N$ two-dimensional array can sustain $N^{1-\epsilon}$ worst-case faults, for any fixed $\epsilon 0$, and still emulate $T$ steps of a fully functioning $N \times N$ array in $O(T+N)$ steps, i.e., with only constant slowdown. Previously, it was known only that an array could tolerate a constant number of faults with constant slowdown. We also show that if faulty nodes are allowed to communicate, but not compute, then an $N$-node one-dimensional array can tolerate $\log^k N$ worst-case faults, for any constant $k 0$, and still emulate a fault-free array with constant slowdown, and this bound is tight.