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This lecture explains how fully explicit expander graphs can reduce the error of randomized algorithms while preserving or nearly preserving their random-bit usage. It analyzes a bipartite-expander method and introduces an expander random-walk approach for exponential error reduction.
Syllabus
Introduction
Error Reduction
Fully Explicit
Strongly Explicit
Algorithm A
Algorithm Analysis
Random Strings
Set B
Set L
Set S
Conclusion
Conclusions
Comparison
Magic trick
Linear error decay
Exponential error decay
Large Expander Graph
Taught by
Ryan O'Donnell