Quality of LP-Based Approximations for Highly Combinatorial Problems

We study the quality of LP-based approximation methods for pure combinatorial problems. We found that the quality of the LPrelaxation is a direct function of the underlying constrainedness of the combinatorial problem. More specifically, we identify a novel phase transition phenomenon in the solution integrality of the relaxation. The solution quality of approximation schemes degrades substantially near phase transition boundaries. Our findings are consistent over a range of LPbased approximation schemes. We also provide results on the extent to which LP relaxations can provide a global perspective of the search space and therefore be used as a heuristic to guide a complete solver.

• Type: Conference
• Year: 2004
• Where: CP
• Authors: Lucian Leahu, Carla P. Gomes
• Keywords: Approximation Schemes, Combinatorial Problem, CP 2004, Phase Transition, Programming Languages