Bounds for Dispersers, Extractors, and Depth-Two Superconcentrators

We show that the size of the smallest depth-two N-superconcentrator is (N log2 N/ log log N). Before this work, optimal bounds were known for all depths except two. For the upper bound, we build superconcentrators by putting together a small number of disperser graphs; these disperser graphs are obtained using a probabilistic argument. For obtaining lower bounds, we present two different methods. First, we show that superconcentrators contain several disjoint disperser graphs. When combined with the lower bound for disperser graphs of Kovari, S

• Type: Journal
• Year: 2000
• Where: SIAMDM
• Authors: Jaikumar Radhakrishnan, Amnon Ta-Shma
• Keywords: Disperser Graphs, Lower Bounds, SIAMDM 2000, Smallest Depth-two N-superconcentrator