NDLI: Towards optimal two-source extractors and Ramsey graphs

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Towards optimal two-source extractors and Ramsey graphs

Content Provider	ACM Digital Library
Author	Cohen, Gil
Abstract	The main contribution of this work is a construction of a two-source extractor for quasi-logarithmic min-entropy. That is, an extractor for two independent n-bit sources with min-entropy O(logn), which is optimal up to the poly(loglogn) factor. A strong motivation for constructing two-source extractors for low entropy is for Ramsey graphs constructions. Our two-source extractor readily yields a $(logn)^{(logloglogn)^{O(1)}}-Ramsey$ graph on n vertices. Although there has been exciting progress towards constructing O(logn)-Ramsey graphs in recent years, a line of work that this paper contributes to, it is not clear if current techniques can be pushed so as to match this bound. Interestingly, however, as an artifact of current techniques, one obtains strongly explicit Ramsey graphs, namely, graphs on n vertices where the existence of an edge connecting any pair of vertices can be determined in time poly(logn). On top of our strongly explicit construction, in this work, we consider algorithms that output the entire graph in poly(n)-time, and make progress towards matching the desired O(logn) bound in this setting. In our opinion, this is a natural setting in which Ramsey graphs constructions should be studied. The main technical novelty of this work lies in an improved construction of an independence-preserving merger (IPM), a variant of the well-studied notion of a merger, which was recently introduced by Cohen and Schulman. Our construction is based on a new connection to correlation breakers with advice. In fact, our IPM satisfies a stronger and more natural property than that required by the original definition, and we believe it may find further applications. .
Starting Page	1157
Ending Page	1170
Page Count	14
File Format	PDF
ISBN	9781450345286
DOI	10.1145/3055399.3055429
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2017-06-19
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Non-malleable extractors Multi-source extractors Ramsey graphs
Content Type	Text
Resource Type	Article

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