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
A lower bound on wait-free counting
Journal of Algorithms
The cube-connected cycles: a versatile network for parallel computation
Communications of the ACM
Distributed, Low Contention Task Allocation
SPDP '96 Proceedings of the 8th IEEE Symposium on Parallel and Distributed Processing (SPDP '96)
Small-depth counting networks and related topics
Small-depth counting networks and related topics
Counting networks with arbitrary fan-out
Distributed Computing
Journal of Parallel and Distributed Computing - Special issue: 18th International parallel and distributed processing symposium
The impact of randomization in smoothing networks
Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
Sorting networks and their applications
AFIPS '68 (Spring) Proceedings of the April 30--May 2, 1968, spring joint computer conference
Near-perfect load balancing by randomized rounding
Proceedings of the forty-first annual ACM symposium on Theory of computing
Hi-index | 0.00 |
A K-smoothing network is a distributed, low-contention data structure where tokens arrive arbitrarily on w input wires and reach w output wires via their completely asynchronous propagation through the network. The maximum discrepancy among the numbers of tokens arriving at the ouput wires, called smoothness, is at most K. It has been a long-standing open problem to construct a K-smoothing network with (i) optimal K, (ii) optimal Θ(log w) depth (called small-depth), (iii) no use of the AKS sorting network, and (iv) no reliance on global initialization. In this work, we present a very simple, randomized network which meets all four desiderata: • It is the cascade of a reasonably small number (about 150) of copies of the simple block network (Dowd et al., JACM'89); hence, it is small-depth and does not use the AKS sorting network. • It achieves smoothness K = 2; hence, it is optimal with respect to smoothness due to a recent improbability result about randomized, small-depth, 1-smoothing networks (Mavronicolas and Sauerwald, PODC'08). • The network is randomized: each balancer is oriented independently and uniformly at random, thus requiring no global initialization. Cascaded before the Θ(log w)-depth 2-counter network due to Klugerman and Plaxton (STOC'92), which does use the AKS sorting network as a building block, our 2-smoothing network yields a new, randomized counting network with depth Θ(log w). The new network is a much simpler alternative to the classical, small-depth counting networks from Klugerman and Plaxton.