Mathematical Programming: Series A and B
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Derandomizing Approximation Algorithms Based on Semidefinite Programming
SIAM Journal on 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
Approximation algorithms for maximization problems arising in graph partitioning
Journal of Algorithms
Computer assisted proof of optimal approximability results
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
A 0.5-Approximation Algorithm for MAX DICUT with Given Sizes of Parts
SIAM Journal on Discrete Mathematics
Approximation of Dense-n/2-Subgraph and the Complement of Min-Bisection
Journal of Global Optimization
A 7/8-Approximation Algorithm for MAX 3SAT?
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
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)
Bounds on the bisection width for random d -regular graphs
Theoretical Computer Science
A modified VNS metaheuristic for max-bisection problems
Journal of Computational and Applied Mathematics
Solving Generalized Maximum Dispersion with Linear Programming
AAIM '07 Proceedings of the 3rd international conference on Algorithmic Aspects in Information and Management
A new Lagrangian net algorithm for solving max-bisection problems
Journal of Computational and Applied Mathematics
Approximating CSPs with global cardinality constraints using SDP hierarchies
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Improved approximation algorithms for maximum graph partitioning problems extended abstract
FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science
Approximation with a fixed number of solutions of some biobjective maximization problems
WAOA'11 Proceedings of the 9th international conference on Approximation and Online Algorithms
Memetic search for the max-bisection problem
Computers and Operations Research
Approximation with a fixed number of solutions of some multiobjective maximization problems
Journal of Discrete Algorithms
Journal of Combinatorial Optimization
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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 the 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, such as 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. All these results may be viewed as extensions of the MAX CUT algorithm of Goemans and Williamson, and the MAX 2-SAT and MAX DI-CUT algorithms of Feige and Goemans.