Almost optimal dispersers

Amnon Ta-Shma

doi:10.1145/276698.276736

Almost optimal dispersers

Amnon Ta-Shma^*

^*Corresponding author for this work

International Computer Science Institute

Research output: Contribution to journal › Conference article › peer-review

15 Scopus citations

Abstract

A (k, ε) disperser graph G = (V₁, V₂, E) is a bipartite graph with the property that any subset A is contained as a subset within V₁ of cardinality K, the neighbor of A cover at least 1-ε fraction of the vertices of V₂. Such graphs have many applications in deramdomization. An explicit construction of (K = 2^k, ε) disperser graphs G = (V = [2ⁿ], W, E) with an almost optimal degree D = poly(n, ε^-1), for every k≥N^Ω(1) is extended for any parameter k≤n.

Original language	English
Pages (from-to)	196-202
Number of pages	7
Journal	Conference Proceedings of the Annual ACM Symposium on Theory of Computing
DOIs	https://doi.org/10.1145/276698.276736
State	Published - 1998
Externally published	Yes
Event	Proceedings of the 1998 30th Annual ACM Symposium on Theory of Computing - Dallas, TX, USA Duration: 23 May 1998 → 26 May 1998

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10.1145/276698.276736

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abstract = "A (k, ε) disperser graph G = (V1, V2, E) is a bipartite graph with the property that any subset A is contained as a subset within V1 of cardinality K, the neighbor of A cover at least 1-ε fraction of the vertices of V2. Such graphs have many applications in deramdomization. An explicit construction of (K = 2k, ε) disperser graphs G = (V = [2n], W, E) with an almost optimal degree D = poly(n, ε-1), for every k≥NΩ(1) is extended for any parameter k≤n.",

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AB - A (k, ε) disperser graph G = (V1, V2, E) is a bipartite graph with the property that any subset A is contained as a subset within V1 of cardinality K, the neighbor of A cover at least 1-ε fraction of the vertices of V2. Such graphs have many applications in deramdomization. An explicit construction of (K = 2k, ε) disperser graphs G = (V = [2n], W, E) with an almost optimal degree D = poly(n, ε-1), for every k≥NΩ(1) is extended for any parameter k≤n.

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Almost optimal dispersers

Abstract

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