ORIE 6334 Spectral Graph Theory December 1 , 2016 Lecture 27 Remix
نویسندگان
چکیده
The proof of the theorem uses a SDP relaxation in terms of vectors vi ∈ Rn for all i ∈ V . Define distances to be d(i, j) ≡ ‖vi − vj‖ and balls to be B(i, r) ≡ {j ∈ V | d(i, j) ≤ r}. We first showed that if there exists a vertex i ∈ V such that |B(i, 1/4)| ≥ n/4, then we can find a cut of sparsity ≤ O(1) ·OPT . If there does not exist such a vertex in V , then we can find U ⊆ V with |U | ≥ n/2 such that for any i ∈ U , 1/4 ≤ ‖vi‖ ≤ 4 and there are at least n/4 vertices j ∈ U such that d(i, j) > 1/4.
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