# .879-approximation algorithms for MAX CUT and MAX 2SAT

@inproceedings{Goemans1994879approximationAF, title={.879-approximation algorithms for MAX CUT and MAX 2SAT}, author={Michel X. Goemans and David P. Williamson}, booktitle={STOC '94}, year={1994} }

We present randomized approximation algorithms for the MAX CUT and MAX 2SAT problems that always deliver solutions of expected value at least .87856 times the optimal value. These algorithms use a simple and elegant technique that randomly rounds the solution to a nonlinear programming relaxation. This relaxation can be interpreted both as a semidefinite program and as an eigenvalue minimization problem. We then show how to derandomize the algorithm to obtain approximation algorithms with the…

## 353 Citations

Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming

- Computer ScienceJACM
- 1995

This algorithm gives the first substantial progress in approximating MAX CUT in nearly twenty years, and represents the first use of semidefinite programming in the design of approximation algorithms.

Improved Approximation Algorithms for Maximum Cut and Satissability Problems Using Semideenite Programming

- Computer Science
- 1995

This algorithm gives the rst substantial progress in approximating MAX CUT in nearly twenty years, and represents the first use of semideenite programming in the design of approximation algorithms.

New 3⁄4 - Approximation Algorithms for MAX SAT

- Computer Science, Mathematics
- 2001

New, simple 3 4-approximational algorithm is presented that applies the probabilistic method/randomized rounding to the solution to a linear programming relaxation of MAX SAT and shows that although standard randomized rounding does not give a good approximate result, the best solution of the two given by randomized rounding and a well-known algorithm of Johnson is always within 3 4 of the optimal solution.

Semidefinite Programming Based Algorithms for the Sparsest Cut Problem

- Computer ScienceRAIRO Oper. Res.
- 2011

This paper analyzed a known relaxation for the Spars- est Cut problem based on positive semidefinite constraints, and presented a branch and bound algorithm and heuristics based on this relaxation, and showed that the proposed strategy leads to a better performance compared to the use of a known semidfinite programming solver.

Sampling subproblems of heterogeneous Max-Cut problems and approximation algorithms

- Computer Science
- 2008

An algorithm is developed and analyzed which uses a novel sampling method to obtain improved bounds for approximating the Max-Cut of a graph and it is shown that by judicious choice of sampling probabilities one can obtain error bounds that are superior to the ones obtained by uniform sampling.

Derandomizing semidefinite programming based approximation algorithms

- Computer Science, MathematicsProceedings of IEEE 36th Annual Foundations of Computer Science
- 1995

This paper gives techniques to derandomize the above class of randomized algorithms, thus obtaining polynomial time deterministic algorithms with the same approximation ratios for the above problems.

Some new randomized approximation algorithms

- Computer Science
- 2000

This thesis designs a polynomial time approximation scheme for the family Max Ek-Function Sat mod p of constraint satisfaction problems for which the domain is Zp, and proves lower bounds on the approximability of Max k-Horn Sat and Max E2-Lin mod p.

Sampling subproblems of heterogeneous Max‐Cut problems and approximation algorithms

- Computer ScienceRandom Struct. Algorithms
- 2008

An algorithm is developed and analyzed which uses a novel sampling method to obtain improved bounds for approximating the Max‐Cut of a graph and it is shown that by judicious choice of sampling probabilities one can obtain error bounds that are superior to the ones obtained by uniform sampling.

z-Approximations

- Computer Science, MathematicsJ. Algorithms
- 2001

Approximation algorithms for NP-hard optimization problems have been widely studied for over three decades. Most of these measure the quality of the solution produced by taking the ratio of the cost…

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