Lower Bounds for Approximating the Matching Polytope
Makrand Sinha · Society for Industrial and Applied Mathematics eBooks · 2018
We prove that any linear program that approximates the matching polytope on n-vertex graphs up to a factor of (1 + ε) for any must have at least inequalities where 0 < α < 1 is an absolute constant. This is tight as exhibited by the (1 + ε) approximating linear program obtained by dropping the odd set constraints of size larger than (1 + ε)/ε from the description of the matching polytope. Previously, a tight lower bound of 2Ω(n) was only known for [22, 5] whereas for , the best lower bound was 2Ω(1/ε) [22]. The key new ingredient in our proof is a close connection to the non-negative rank of a lopsided version of the unique disjointness matrix.