A guided tour of Chernoff bounds
Information Processing Letters
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Fast deflection routing for packets and worms
PODC '93 Proceedings of the twelfth annual ACM symposium on Principles of distributed computing
Universal algorithms for store-and-forward and wormhole routing
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Universal packet routing algorithms
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
A theory of wormhole routing in parallel computers
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
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In this paper we consider wormhole routing in a d-dimensional torus of side length n. In particular, we present an optimal randomized algorithm for routing worms of length up to O(n/(d log n)^2), one per node, to random destinations. Previous algorithms only work optimally for two dimensions, or are a factor of log n away from the optimal running time. As a by-product, we develop an algorithm for the 2-dimensional torus that guarantees an optimal runtime for worms of length up to O(n/(log n)^2) with much higher probability than all previous algorithms.