On Small-Depth Tree Augmentations

Abstract

We study the Weighted Tree Augmentation Problem for general link costs. We show that the integrality gap of the ODD-LP relaxation for the (weighted) Tree Augmentation Problem for a k-level tree instance is at most 2 − 1 2 k−1 . For 2-and 3-level trees, these ratios are 3 2 and 7 4 respectively. Our proofs are constructive and yield polynomial-time approximation algorithms with matching guarantees.