Greedily finding a dense subgraph
Journal of Algorithms
Derandomizing Approximation Algorithms Based on Semidefinite Programming
SIAM Journal on Computing
Approximation algorithms for maximization problems arising in graph partitioning
Journal of Algorithms
A 0.5-Approximation Algorithm for MAX DICUT with Given Sizes of Parts
SIAM Journal on Discrete Mathematics
Random Structures & Algorithms - Probabilistic methods in combinatorial optimization
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
The RPR2 Rounding Technique for Semidefinite Programs
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Finding Dense Subgraphs with Semidefinite Programming
APPROX '98 Proceedings of the International Workshop on Approximation Algorithms for Combinatorial Optimization
On the densest k-subgraph problems
On the densest k-subgraph problems
Approximation algorithms for the bi-criteria weighted MAX-CUT problem
Discrete Applied Mathematics
On the complexity of global constraint satisfaction
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
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In this paper we improve the analysis of approximation algorithms based on semidefinite programming for the maximum graph partitioning problems MAX-k-CUT, MAX- k -UNCUT, MAX- k -DIRECTED-CUT, MAX -k-DIRECTED-UNCUT, MAX- k -DENSE-SUBGRAPH, and MAX-k-VERTEX-COVER.It was observed by Han, Ye, Zhang (2002) and Halperin, Zwick (2002) that a parameter-driven random hyperplane can lead to better approximation factors than obtained by Goemans and Williamson (1994). Halperin and Zwick could describe the approximation factors by a mathematical optimization problem for the above problems for $k=\frac{n}{2}$ and found a choice of parameters in a heuristic way. The innovation of this paper is twofold. First, we generalize the algorithm of Halperin and Zwick to cover all cases of k, adding some algorithmic features. The hard work is to show that this leads to a mathematical optimization problem for an optimal choice of parameters. Secondly, as a key-step of this paper we prove that a sub-optimal set of parameters is determined by a linear program. Its optimal solution computed by CPLEX leads to the desired improvements. In this fashion a more systematic analysis of the semidefinite relaxation scheme is obtained which leaves room for further improvements.