Integrality gap of the Cut LP for WTAP below 2

Determine whether the integrality gap of the Cut LP relaxation for the Weighted Tree Augmentation Problem is strictly less than 2 by establishing an explicit upper bound below 2 on this integrality gap.

Background

The Cut LP is the classic linear programming relaxation for the Weighted Tree Augmentation Problem (WTAP). It is known to have an integrality gap of at most 2 via standard arguments, and there is a lower bound of 1.5 due to Cheriyan, Karloff, Khandekar, and Kőnemann. However, despite extensive study of WTAP, no better-than-2 upper bound on the integrality gap of the Cut LP is known.

This paper designs a stronger LP and rounding achieving a 1.49-approximation, demonstrating that improved bounds are possible for enhanced relaxations. Nevertheless, determining whether the natural Cut LP itself admits an integrality gap strictly below 2 remains unresolved.