A randomized, o(log w)-depth 2 smoothing network

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 longstanding open problem to construct a K-smoothing network with (i) optimal K, (ii) optimal Θ(lg w) depth (called smalldepth), (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 [6]; 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 from [...

• Type: Conference
• Year: 2009
• Where: SPAA
• Authors: Marios Mavronicolas, Thomas Sauerwald
• Keywords: AKS Sorting Network, Computer Science, Randomized Counting Network, Simple Block Network, SPAA 2009