Lower Bounds and Exact Algorithms for the Graph Partitioning Problem Using Multicommodity Flows
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
Finding optimal solutions to the graph partitioning problem with heuristic search
Annals of Mathematics and Artificial Intelligence
Exploiting semidefinite relaxations in constraint programming
Computers and Operations Research
Simplified infeasible interior-point algorithm for SDO using full Nesterov-Todd step
Numerical Algorithms
Memetic search for the max-bisection problem
Computers and Operations Research
A branch-and-bound algorithm for the minimum cut linear arrangement problem
Journal of Combinatorial Optimization
A memetic approach for the max-cut problem
PPSN'12 Proceedings of the 12th international conference on Parallel Problem Solving from Nature - Volume Part II
Better bounds for graph bisection
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Solving large scale Max Cut problems via tabu search
Journal of Heuristics
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An exact solution method for the graph bisection problem is presented. We describe a branch-and-bound algorithm which is based on a cutting plane approach combining semidefinite programming and polyhedral relaxations. We report on extensive numerical experiments which were performed for various classes of graphs. The results indicate that the present approach solves general problem instances with 80--90 vertices exactly in reasonable time and provides tight approximations for larger instances. Our approach is particularly well suited for special classes of graphs as planar graphs and graphs based on grid structures.