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2-Source Dispersers for no(1) Entropy, and Ramsey Graphs Beating

Summary: 2-Source Dispersers for no(1)
Entropy, and Ramsey Graphs Beating
the Frankl-Wilson Construction
Boaz Barak
Anup Rao
Ronen Shaltiel
Avi Wigderson§
July 22, 2008
The main result of this paper is an explicit disperser for two independent sources on n bits,
each of min-entropy k = 2log1-0 n
, for some small absolute constant 0 > 0). Put differently,
setting N = 2n
and K = 2k
, we construct an explicit N × N Boolean matrix for which no K × K
sub-matrix is monochromatic. Viewed as the adjacency matrix of a bipartite graph, this gives an
explicit construction of a bipartite K-Ramsey graph of 2N vertices.
This improves the previous the previous bound of k = o(n) of Barak, Kindler, Shaltiel, Sudakov
and Wigderson [BKS+
05]. As a corollary, we get a construction of a 22log1-0 n


Source: Anderson, Richard - Department of Computer Science and Engineering, University of Washington at Seattle
Shaltiel, Ronen - Department of Computer Science, University of Haifa


Collections: Computer Technologies and Information Sciences