Almost optimal dispersers

Amnon Ta-Shma

doi:10.1007/s004930200006

Almost optimal dispersers

Amnon Ta-Shma^*

^*Corresponding author for this work

School of Computer Science and AI

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

A (K, ε) disperser is a bipartite graph G= (V₁, V₂, E) with the property that every subset A of V₁ of cardinality at least K, has at least 1-ε fraction of the vertices of V₂ as neighbors. Such graphs have many applications in derandomization. Saks, Srinivasan and Zhou presented an explicit construction of a (K = 2^k, ε) disperser G: (V₁ = [2ⁿ], V₂, E) with an almost optimal degree D = poly(n/ε), for every k ≥ n^ω(1). We extend their result for every parameter k ≥ poly log (n/ε).

Original language	English
Pages (from-to)	123-145
Number of pages	23
Journal	Combinatorica
Volume	22
Issue number	1
DOIs	https://doi.org/10.1007/s004930200006
State	Published - 2002

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abstract = "A (K, ε) disperser is a bipartite graph G= (V1, V2, E) with the property that every subset A of V1 of cardinality at least K, has at least 1-ε fraction of the vertices of V2 as neighbors. Such graphs have many applications in derandomization. Saks, Srinivasan and Zhou presented an explicit construction of a (K = 2k, ε) disperser G: (V1 = [2n], V2, E) with an almost optimal degree D = poly(n/ε), for every k ≥ nω(1). We extend their result for every parameter k ≥ poly log (n/ε).",

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Almost optimal dispersers

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