A Unified theory of interconnection network structure
Theoretical Computer Science
Sorting in c log n parallel steps
Combinatorica
The periodic balanced sorting network
Journal of the ACM (JACM)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Journal of the ACM (JACM)
Coins, weights and contention in balancing networks
PODC '94 Proceedings of the thirteenth annual ACM symposium on Principles of distributed computing
Parallel and Distributed Computation: Numerical Methods
Parallel and Distributed Computation: Numerical Methods
Distributed, Low Contention Task Allocation
SPDP '96 Proceedings of the 8th IEEE Symposium on Parallel and Distributed Processing (SPDP '96)
IPPS '98 Proceedings of the 12th. International Parallel Processing Symposium on International Parallel Processing Symposium
Small-depth counting networks and related topics
Small-depth counting networks and related topics
Journal of Parallel and Distributed Computing - Special issue: 18th International parallel and distributed processing symposium
The Art of Multiprocessor Programming
The Art of Multiprocessor Programming
Near-perfect load balancing by randomized rounding
Proceedings of the forty-first annual ACM symposium on Theory of computing
Smoothed Analysis of Balancing Networks
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
A randomized, o(log w)-depth 2 smoothing network
Proceedings of the twenty-first annual symposium on Parallelism in algorithms and architectures
Theoretical Computer Science
Hi-index | 0.00 |
We revisit smoothing networks which are made up of balancers and wires. Tokens arrive arbitrarily on w input wires and propagate asynchronously through the network; each token gets service on the output wire it arrives at. The smoothness is the maximum discrepancy among the numbers of tokens arriving at the w output wires. We assume that balancers are oriented independently and uniformly at random. We present a collection of lower and upper bounds on smoothness, which are to some extent surprising:-The smoothness of a single block network is log log w + Θ(1) (with high probability), where the additive constant is between -2 and 4. This tight bound improves vastly over the upper bound of O(√log w) from Herlihy and Tirthapura, and it significantly improves our understanding of the smoothing properties of the block network. -Most significantly, the smoothness of the cascade of two block networks is no more than 16 (with high probability); this is the first known randomized network with so small depth (2 log w) and so good smoothness. The proof introduces some novel combinatorial and probabilistic structures and techniques which may be further applicable. This result demonstrates the full power of randomization in smoothing networks. -There is no randomized 1-smoothing network of width w and depth d that achieves 1-smoothness with probability better than d/w-1. In view of the deterministic 1-smoothing network from Klugerman and Plaxton, this result implies the first separation between deterministic and randomized smoothing networks, which demonstrates an unexpected limitation of randomization: it can get to constant smoothness very easily, but after that, the progress to 1-smoothing is very limited.