NDLI: Two-source dispersers for polylogarithmic entropy and improved ramsey graphs

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Two-source dispersers for polylogarithmic entropy and improved ramsey graphs

Content Provider	ACM Digital Library
Author	Cohen, Gil
Abstract	In his influential 1947 paper that inaugurated the probabilistic method, Erdős proved the existence of 2logn-Ramsey graphs on n vertices. Matching Erdős’ result with a constructive proof is considered a central problem in combinatorics, that has gained a significant attention in the literature. The state of the art result was obtained in the celebrated paper by Barak, Rao, Shaltiel, and Wigderson who constructed a $2^{2^{(loglogn)^{1−α}}}-Ramsey$ graph, for some small universal constant α > 0. In this work, we significantly improve this result and construct $2^{(loglogn)^{c}}-Ramsey$ graphs, for some universal constant c. In the language of theoretical computer science, this resolves the problem of explicitly constructing dispersers for two n-bit sources with entropy (n). In fact, our disperser is a zero-error disperser that outputs a constant fraction of the entropy. Prior to this work, such dispersers could only support entropy Ω(n). .
Starting Page	278
Ending Page	284
Page Count	7
File Format	PDF
ISBN	9781450341325
DOI	10.1145/2897518.2897530
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2016-06-19
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Explicit constructions Dispersers Ramsey graphs
Content Type	Text
Resource Type	Article

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