Experiments in quadratic 0-1 programming
Mathematical Programming: Series A and B
Parallel branch and bound algorithms for quadratic zero-one programs on the hypercube architecture
Annals of Operations Research
.879-approximation algorithms for MAX CUT and MAX 2SAT
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Laplacian eigenvalues and the maximum cut problem
Mathematical Programming: Series A and B
Solving the max-cut problem using eigenvalues
Discrete Applied Mathematics - Special volume on partitioning and decomposition in combinatorial optimization
Adaptive Memory Tabu Search for Binary Quadratic Programs
Management Science
Solving quadratic (0,1)-problems by semidefinite programs and cutting planes
Mathematical Programming: Series A and B
Fixing Variables in Semidefinite Relaxations
SIAM Journal on Matrix Analysis and Applications
New approaches for optimizing over the semimetric polytope
Mathematical Programming: Series A and B
Using a Mixed Integer Quadratic Programming Solver for the Unconstrained Quadratic 0-1 Problem
Mathematical Programming: Series A and B
Minimizing breaks by maximizing cuts
Operations Research Letters
An optimal sdp algorithm for max-cut, and equally optimal long code tests
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Duality Gap Estimation of Linear Equality Constrained Binary Quadratic Programming
Mathematics of Operations Research
An iterative scheme for valid polynomial inequality generation in binary polynomial programming
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
Exact bipartite crossing minimization under tree constraints
SEA'10 Proceedings of the 9th international conference on Experimental Algorithms
An exact solution method for unconstrained quadratic 0---1 programming: a geometric approach
Journal of Global Optimization
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In this paper we present a method for finding exact solutions of the Max-Cut problem max xTLxsuch that x茂戮驴 { 茂戮驴 1,1}n. We use a semidefinite relaxation combined with triangle inequalities, which we solve with the bundle method. This approach is due to [12] and uses Lagrangian duality to get upper bounds with reasonable computational effort. The expensive part of our bounding procedure is solving the basic semidefinite programming relaxation of the Max-Cut problem.We review other solution approaches and compare the numerical results with our method. We also extend our experiments to unconstrained quadratic 0-1 problems and to instances of the graph bisection problem.The experiments show, that our method nearly always outperforms all other approaches. Our algorithm, which is publicly accessible through the Internet, can solve virtually any instance with about 100 variables in a routine way.