Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
Gadgets, Approximation, and Linear Programming
SIAM Journal on Computing
Approximation algorithms
Some optimal inapproximability results
Journal of the ACM (JACM)
Approximation algorithms for maximization problems arising in graph partitioning
Journal of Algorithms
Approximation Algorithms for Maximum Coverage and Max Cut with Given Sizes of Parts
Proceedings of the 7th International IPCO Conference on Integer Programming and Combinatorial Optimization
Approximating almost all instances of MAX-CUT within a ratio above the håstad threshold
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
ESA'05 Proceedings of the 13th annual European conference on Algorithms
| Hi-index | 0.00 |
We present polynomial time randomized approximation algorithms with non trivial performance guarantees for the problem of partitioning the vertices of a weighted graph into two sets of sizes that differ at most by a given threshold B, so as to maximize the weight of the crossing edges. For B equal to 0 this problem is known as Max Bisection, whereas for B equal to the number n of nodes it is the Maximum Cut problem. The approximation results are obtained by extending the methodology used by Y. Ye for Max Bisection and by combining this technique with another one that uses the algorithm of Goemans and Williamson for the Maximum Cut problem. When B is equal to zero the approximation ratio achieved coincides with the one obtained by Y. Ye; otherwise it is always above this value and tends to the value obtained by Goemans and Williamson as B approaches the number n of nodes.