Strong reductions for extended formulations
G\'abor Braun, Sebastian Pokutta, Aurko Roy
TL;DR
This paper extends reduction techniques for linear and semidefinite programming, leading to new hardness results and a strong integrality gap for the IndependentSet problem, challenging the tightness of the Lasserre hierarchy.
Contribution
It generalizes reduction mechanisms to fractional optimization and relaxes affineness, resulting in new hardness proofs and a significant integrality gap for IndependentSet.
Findings
New LP-hardness and SDP-hardness results for classical problems
A very strong Lasserre integrality gap for IndependentSet
Demonstration that Lasserre hierarchy does not always yield tight relaxations
Abstract
We generalize the reduction mechanism for linear programming problems and semidefinite programming problems from [arXiv:1410.8816] in two ways 1) relaxing the requirement of affineness and 2) extending to fractional optimization problems. As applications we provide several new LP-hardness and SDP-hardness results, e.g., for the SparsestCut problem, the BalancedSeparator problem, the MaxCut problem and the Matching problem on 3-regular graphs. We also provide a new, very strong Lasserre integrality gap result for the IndependentSet problem, which is strictly greater than the best known LP approximation, showing that the Lasserre hierarchy does not always provide the tightest SDP relaxation.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.