Efficient Schemes for Parallel Communication
Journal of the ACM (JACM)
Routing, merging, and sorting on parallel models of computation
Journal of Computer and System Sciences
On the power of two-point based sampling
Journal of Complexity
Randomized parallel communication (Preliminary Version)
PODC '82 Proceedings of the first ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Randomized algorithms and pseudorandom numbers
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Tight bounds for oblivious routing in the hypercube
SPAA '90 Proceedings of the second annual ACM symposium on Parallel algorithms and architectures
Fast algorithms for bit-serial routing on a hypercube
SPAA '90 Proceedings of the second annual ACM symposium on Parallel algorithms and architectures
Randomness in private computations
PODC '96 Proceedings of the fifteenth annual ACM symposium on Principles of distributed computing
On the Dealer‘s Randomness Required in Secret Sharing Schemes
Designs, Codes and Cryptography
Randomness vs. fault-tolerance
PODC '97 Proceedings of the sixteenth annual ACM symposium on Principles of distributed computing
Amortizing randomness in private multiparty computations
PODC '98 Proceedings of the seventeenth annual ACM symposium on Principles of distributed computing
A Randomnesss-Rounds Tradeoff in Private Computation
CRYPTO '94 Proceedings of the 14th Annual International Cryptology Conference on Advances in Cryptology
Optimal oblivious routing on d-dimensional meshes
Theoretical Computer Science - Foundations of software science and computation structures
A Lower Bound for Oblivious Dimensional Routing
Euro-Par '09 Proceedings of the 15th International Euro-Par Conference on Parallel Processing
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Three parameters characterize the performance of a probabilistic algorithm: T, the runtime of the algorithm; Q, the probability that the algorithm fails to complete the computation in the first T steps and R, the amount of randomness used by the algorithm, measured by the entropy of its random source.We present a tight tradeoff between these three parameters for the problem of oblivious packet routing on N-vertex bounded-degree networks. We prove a (1 - Q) log N/T - log Q - &Ogr;(1) lower bound for the entropy of a random source of any oblivious packet routing algorithm that routes an arbitrary permutation in T steps with probability 1 - Q. We show that this lower bound is almost optimal by proving the existence, for every e3 log N ≤ T ≤ N1/2, of an oblivious algorithm that terminates in T steps with probability 1 - Q and uses (1-Q+&ogr;(1))logN/T-logQ independent random bits.We complement this result with an explicit construction of a family of oblivious algorithms that use less than a factor of log N more random bits than the optimal algorithm achieving the same run-time.