Integer and combinatorial optimization
Integer and combinatorial optimization
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Pruning by Isomorphism in Branch-and-Cut
Proceedings of the 8th International IPCO Conference on Integer Programming and Combinatorial Optimization
On the Satisfiability of Symmetrical Constrained Satisfaction Problems
ISMIS '93 Proceedings of the 7th International Symposium on Methodologies for Intelligent Systems
Breaking Row and Column Symmetries in Matrix Models
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
A cutting plane algorithm for graph coloring
Discrete Applied Mathematics
Packing and partitioning orbitopes
Mathematical Programming: Series A and B
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
A measure & conquer approach for the analysis of exact algorithms
Journal of the ACM (JACM)
CPAIOR '09 Proceedings of the 6th International Conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Propagation algorithms for lexicographic ordering constraints
Artificial Intelligence
A Branch-and-Cut algorithm for graph coloring
Discrete Applied Mathematics - Special issue: IV ALIO/EURO workshop on applied combinatorial optimization
Constraint integer programming: a new approach to integrate CP and MIP
CPAIOR'08 Proceedings of the 5th international conference on Integration of AI and OR techniques in constraint programming for combinatorial optimization problems
Static and dynamic structural symmetry breaking
Annals of Mathematics and Artificial Intelligence
On the complexity and completeness of static constraints for breaking row and column symmetry
CP'10 Proceedings of the 16th international conference on Principles and practice of constraint programming
Mathematical Programming: Series A and B
Branch-cut-and-propagate for the maximum k-colorable subgraph problem with symmetry
CPAIOR'11 Proceedings of the 8th international conference on Integration of AI and OR techniques in constraint programming for combinatorial optimization problems
Conflict analysis in mixed integer programming
Discrete Optimization
Symmetric ILP: Coloring and small integers
Discrete Optimization
Branch-cut-and-propagate for the maximum k-colorable subgraph problem with symmetry
CPAIOR'11 Proceedings of the 8th international conference on Integration of AI and OR techniques in constraint programming for combinatorial optimization problems
The maximum k-colorable subgraph problem and orbitopes
Discrete Optimization
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Given an undirected graph and a positive integer k, themaximum k-colorable subgraph problem consists of selecting a k-colorable induced subgraph of maximum cardinality. The natural integer programming formulation for this problem exhibits two kinds of symmetry: arbitrarily permuting the color classes and/or applying a non-trivial graph automorphism gives equivalent solutions. It is well known that such symmetries have negative effects on the performance of constraint/integer programming solvers. We investigate the integration of a branch-and-cut algorithm for solving the maximum k-colorable subgraph problem with constraint propagation techniques to handle the symmetry arising from the graph. The latter symmetry is handled by (non-linear) lexicographic ordering constraints and linearizations thereof. In experiments, we evaluate the influence of several components of our algorithm on the performance, including the different symmetry handling methods. We show that several components are crucial for an efficient algorithm; in particular, the handling of graph symmetries yields a significant performance speed-up.