Fences Are Futile: On Relaxations for the Linear Ordering Problem

  • Alantha Newman
  • Santosh Vempala
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2081)


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.


Label Edge Forward Edge Variable Gadget Clause Gadget Linear Order Problem 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Alantha Newman
    • 1
  • Santosh Vempala
    • 2
  1. 1.Laboratory for Computer ScienceMassachusetts Institute of TechnologyCambridgeUK
  2. 2.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUK

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