On the partial order polytope of a digraph
Mathematical Programming: Series A and B
Mathematical Programming: Series A and B
Some optimal inapproximability results
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
The Interval Order Polytope of a Digraph
Proceedings of the 4th International IPCO Conference on Integer Programming and Combinatorial Optimization
The Strongest Facets of the Acyclic Subgraph Polytope Are Unknown
Proceedings of the 5th International IPCO Conference on Integer Programming and Combinatorial Optimization
The Maximum Acyclic Subgraph Problem and Degree-3 Graphs
APPROX '01/RANDOM '01 Proceedings of the 4th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems and 5th International Workshop on Randomization and Approximation Techniques in Computer Science: Approximation, Randomization and Combinatorial Optimization
Revised GRASP with path-relinking for the linear ordering problem
Journal of Combinatorial Optimization
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We study polyhedral relaxations for the linear ordering problem. The integrality gap for the standard linear programming relaxation is 2. Our main result is that the integrality gap remains 2 even when the standard relaxations are augmented with k-fence constraints for any k, and with k-Möbius ladder constraints for k up to 7; when augmented with k-Möbius ladder constraints for general k, the gap is at least 33/17 ≅ 1:94. Our proof is non-constructive-we obtain an extremal example via the probabilistic method. Finally, we show that no relaxation that is solvable in polynomial time can have an integrality gap less than 66/65 unless P=NP.