# Randomized Rounding for Semidefinite Programs-Variations on the MAX CUT Example

@inproceedings{Feige1999RandomizedRF, title={Randomized Rounding for Semidefinite Programs-Variations on the MAX CUT Example}, author={Uriel Feige}, booktitle={RANDOM-APPROX}, year={1999} }

MAX CUT is the problem of partitioning the vertices of a graph into two sets, maximizing the number of edges joining these sets. Goemans and Williamson gave an algorithm that approximates MAX CUT within a ratio of 0.87856. Their algorithm first uses a semidefinite programming relaxation of MAX CUT that embeds the vertices of the graph on the surface of an n dimensional sphere, and then cuts the sphere in two at random.

## 9 Citations

### On the optimality of the random hyperplane rounding technique for MAX CUT

- Computer Science, MathematicsRandom Struct. Algorithms
- 2002

There are graphs and optimal embeddings for which the best hyperplane approximates opt within a ratio no better than α, even in the presence of additional valid constraints, which strengthens a result of Karloff that applied only to the expected number of edges cut by a random hyperplane.

### More on Max Cut

- Computer Science

The max-cut algorithm of Goemans and Williamson is studied more closely and triangle constraints described below seem promising, which may strengthen the SDP by additional constraint that are valid for true 1 solutions.

### 23.1 Improving Convex Programming Relaxations

- Computer Science
- 2005

In past lectures we’ve learned that we write integer linear program (ILP) formulations to model hard problems exactly. But since these programs are too hard to solve, we relax them into linear…

### A new point of NP-hardness for unique games

- Computer ScienceSTOC '12
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For these c, this is the first hardness result showing that it helps to take the alphabet size larger than 2 and the NP-hardness reductions are quasilinear-size and thus show nearly full exponential time is required, assuming the ETH.

### CS 6550 – Design and Analysis of Algorithms Professor :

- Mathematics
- 2007

We present a surprising result that the traveling salesman problem has a polynomial-time approximation scheme when the distances between cities are Euclidean. This result, independently due to Arora…

### Social choice, computational complexity, Gaussian geometry, and Boolean functions

- MathematicsArXiv
- 2014

A web of connections between the mathematical theory of voting and social choice; the computational complexity of the Maximum Cut problem; the Gaussian Isoperimetric Inequality and Borell's generalization thereof; the Hypercontractive Inequality of Bonami; and, the analysis of Boolean functions are described.

### Optimal inapproximability results for MAX-CUT and other 2-variable CSPs?

- Computer Science, Physics45th Annual IEEE Symposium on Foundations of Computer Science
- 2004

Though it is unable to prove the majority is stablest conjecture, some partial results are enough to imply that MAX-CUT is hard to (3/4 + 1/(2/spl pi/) + /spl epsi/)-approximate (/spl ap/ .909155), assuming only the unique games conjecture.

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