Approximating (Unweighted) Tree Augmentation via Lift-and-Project (Part 0: $1.8+\epsilon$ approximation for (Unweighted) TAP)
Abstract
We study the unweighted Tree Augmentation Problem (TAP) via the Lasserre (Sum of Squares) system. We prove an approximation guarantee of () relative to an SDP relaxation, which matches the combinatorial approximation guarantee of Even, Feldman, Kortsarz and Nutov in ACM TALG (2009), where is a constant. We generalize the combinatorial analysis of integral solutions of Even, et al., to fractional solutions by identifying some properties of fractional solutions of the Lasserre system via the decomposition result of Rothvo{\ss} (arXiv:1111.5473, 2011) and Karlin, Mathieu and Nguyen (IPCO 2011).
Keywords
Cite
@article{arxiv.1604.00708,
title = {Approximating (Unweighted) Tree Augmentation via Lift-and-Project (Part 0: $1.8+\epsilon$ approximation for (Unweighted) TAP)},
author = {Joe Cheriyan and Zhihan Gao},
journal= {arXiv preprint arXiv:1604.00708},
year = {2016}
}
Comments
This is a manuscript from July 2014 that was widely circulated but was not posted on the web. It is being posted for the sake of archiving/referencing. The results have been subsumed by arXiv:1507.01309 by the same authors. 15 pages, 1 figure