Integrality gap of the Odd Cut LP for WTAP below 2

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

Background

The Odd Cut LP, introduced by Fiorini, Groß, Kőnemann, and Sanitá, strengthens the Cut LP and is solvable in polynomial time. It is known to be integral for WTAP instances containing only up-links and cross-links, but its worst-case integrality gap on general WTAP instances is unknown.

Establishing whether the Odd Cut LP has integrality gap strictly below 2 would clarify how much strength this relaxation provides compared to the Cut LP and could guide the design of improved LP-based algorithms for WTAP.

References

In 2018, Fiorini, Groß, Könemann, and Sanità introduced the Odd Cut LP, which is a stronger relaxation for WTAP and is a key starting point for this work. It is still unknown whether this stronger LP has an integrality gap below 2.

— A Strong Linear Programming Relaxation for Weighted Tree Augmentation  (2603.29582 - Cohen-Addad et al., 31 Mar 2026) in Introduction