Effect of intermediate per-vertex relaxations on the rounding constant

Determine whether strengthening the EKS14 relaxation by adding per-vertex valid inequalities that remain strictly between the EKS14 relaxation and the configuration linear program improves the approximation constant of the Wang–Sitters rounding framework.

Background

The paper observes that per-vertex strengthening inequalities, including the set constraints considered by Schwartz and Yeheskel, are implied by the configuration linear program. Consequently, such strengthenings lie between the EKS14 relaxation used by the Wang–Sitters scheme and the configuration relaxation. The paper does not determine whether using a relaxation from this intermediate class reduces the constant produced by the rounding procedure.