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Summary: Com S 633: Randomness in Computation
Lecture 15 Scribe: Rakesh Setty
1 Derandomizing MaxCut algorithm using Pairwise Indepen-
dent Generator
In the last class, we de ned (m; t; l) pairwise independent generator as a function
f : m ! tl such that
8i 6= j; 8 ; 2 t
Pr
x 2 m
[f i (x) = ^ f j (x) = ] = 1
2 2t
We also proved the following theorem.
Theorem: 8t; 8l; 8m with 2 m > l and m t, there is (2m; t ; l) pairwise independent generator.
Now, we show the following algorithm to derandomize Max Cut algorithm.
1. Input G = (V; E) where jV j = n
2. Let f be a (2logn ; 1; n) pairwise independent generator.
3. Input G = (V; E) where jV j = n
4. Randomly pick a 2logn bit string (call x)
5. A ; B
6. for i 1 to n
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