On Small-Depth Tree Augmentations

10/30/2021

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by   Ojas Parekh, et al.

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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.