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Almost Optimal Dispersers.pdf

T.combinatorica.02.pdf

🔗 Source: cs.tau.ac.il

📊 Size: 306 KB

👤 Author: Amnon Ta-Shma

⬇️ Downloads: 60

Summary

Key Contributions:

1. Improved Scope: The construction works for larger values of k compared to [11], who required k ≥ n^(1/6).

2. Reduced Entropy Loss: Achieves polylog(n/ϵ) entropy loss, a significant improvement over the n^(1/6) loss in [11].

Technical Overview:

Disperser Definition: A bipartite graph G=(V1, V2, E) is a (K, ϵ) disperser if every subset A of V1 with |A| ≥ K has at least (1-ϵ)|V2| distinct neighbors in V2.

Extractors and Dispersers: The paper leverages the connection between extractors (a generalization of dispersers) and explicit constructions, using a block-wise extractor as a building block.

Construction: The main idea is to construct a bipartite graph with carefully chosen degrees, leveraging probabilistic arguments and techniques from previous work.

Significance:

This result has implications for various applications requiring strong random-like properties, such as:

Deterministic amplification
Oblivious sampling
Leader election
Hardness of approximating loglogClique
Explicit constructions of a-expanding graphs and non-blocking networks.

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Description

Saks, Srinivasan and Zhou's construction of almost optimal dispersers is extended for any parameter \( k \geq \text{polylog}(n/\epsilon) \), providing bipartite graphs with strong random-like properties.

Technical Information

File Format: PDF
File Size: 306 KB
Pages: 23
Language: EN
Author: Amnon Ta-Shma
Total Downloads: 60
Last Updated: 6 hours ago

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