STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
On the integrality ratio of semidefinite relaxations of MAX CUT
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Approximating the value of two power proof systems, with applications to MAX 2SAT and MAX DICUT
ISTCS '95 Proceedings of the 3rd Israel Symposium on the Theory of Computing Systems (ISTCS'95)
Improved Approximation of MAX-CUT on Graphs of Bounded Degree
Improved Approximation of MAX-CUT on Graphs of Bounded Degree
A Note on Approximating MAX-BISECTION on Regular Graphs
A Note on Approximating MAX-BISECTION on Regular Graphs
Approximating Min-sum Set Cover
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
A new PCP outer verifier with applications to homogeneous linear equations and max-bisection
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Approximation Algorithms for Max 3-Section Using Complex Semidefinite Programming Relaxation
COCOA '09 Proceedings of the 3rd International Conference on Combinatorial Optimization and Applications
On the complexity of global constraint satisfaction
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Complexity of approximating CSP with balance / hard constraints
Proceedings of the 5th conference on Innovations in theoretical computer science
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We obtain improved semidefinite programming based approximation algorithms for all the natural maximum bisection problems of graphs. Among the problems considered are: MAX n/2 -BISECTION - partition the vertices of a graph into two sets of equal size such that the total weight of edges connecting vertices from different sides is maximized; MAX n/2 -VERTEX-COVER - find a set containing half of the vertices such that the total weight of edges touching this set is maximized; MAX n/2 -DENSE-SUBGRAPH - find a set containing half of the vertices such that the total weight of edges connecting two vertices from this set is maximized; and MAX n/2 -UnCUT - partition the vertices into two sets of equal size such that the total weight of edges that do not cross the cut is maximized. We also consider the directed versions of these problems, MAX n/2 -DIRECTED-BISECTION and MAX n/2 -DIRECTED-UnCUT. These results can be used to obtain improved approximation algorithms for the unbalanced versions of the partition problems mentioned above, where we want to partition the graph into two sets of size k and n - k, where k is not necessarily n/2 . Our results improve, extend and unify results of Frieze and Jerrum, Feige and Langberg, Ye, and others.