Lecture 14 : Semidefinite Programming and Max - Cut
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چکیده
In the Maximum Cut problem, we are given a weighted graph G = (V,E,W ). The goal is to find a partitioning (S, S̄), S ⊂ V of the graph so as to maximize the total weight of edges in the cut. Formally the problem is to find f : V → {0, 1} which maximizes∑ij∈E:f(i)6=f(j) wij . In homework #1, we already saw a greedy 1/2-approximation algorithm for this problem. Now let’s examine a potential LP formulation.
منابع مشابه
Semidefinite Programming Part 2
2. Max-Cut Revisited As in last week’s lecture, we approximate solutions to Max-Cut using Goemans’s and Williamson’s αGW = 0.878-approximation. Specifically, we seek max ∑ (i,j)∈E 1 4 ∥∥vi − vj∥∥2 subject to the constraint that ∀i, ‖vi‖ = 1. We can visualize this by drawing the vectors restricted to a unit circle, as seen in the figure to the left. There is an appealing geometric intuition here...
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تاریخ انتشار 2008