# Approximating (Unweighted) Tree Augmentation via Lift-and-Project, Part II

@article{Cheriyan2017ApproximatingT, title={Approximating (Unweighted) Tree Augmentation via Lift-and-Project, Part II}, author={J. Cheriyan and Zhihan Gao}, journal={Algorithmica}, year={2017}, volume={80}, pages={608-651} }

In Part II, we study the unweighted tree augmentation problem (TAP) via the Lasserre (sum of squares) system. We prove that the integrality ratio of an SDP relaxation (the Lasserre tightening of an LP relaxation) is $$\le \frac{3}{2}+\epsilon $$≤32+ϵ, where $$\epsilon >0$$ϵ>0 can be any small constant. We obtain this result by designing a polynomial-time algorithm for TAP that achieves an approximation guarantee of ($$\frac{3}{2}+\epsilon $$32+ϵ) relative to the SDP relaxation. The algorithm is… Expand

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#### 22 Citations

Improved Approximation for Weighted Tree Augmentation with Bounded Costs

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An LP based $(\delta+\epsilon)-approximation for WTAP restricted to cost vectors in $[1,M]^L$ for $\delta \approx 1.96417$ and for the special case of TAP this factor is improved to $\frac{5}{3}+\ epsilon$. Expand

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Adjiashvili’s approximation to a 3 2 + ε-approximation for WTAP under the bounded cost assumption is improved by introducing a strong LP that combines. Expand

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The weighted tree augmentation problem (WTAP) is a fundamental network design problem. We are given an undirected tree $G = (V,E)$, an additional set of edges $L$ called links and a cost vector $c… Expand

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This work presents the first improved approximation algorithm for WTAP in more than three decades and improves this factor to 5/3+ε, which is the ratio between the largest and the smallest cost of any link. Expand

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This paper shows that in weighted TAP, the goal is to augment a tree with a minimum cost set of edges such that the graph becomes two edge connected, and gives two different top-down coloring algorithms which will be useful in eventually resolving the integrality gap of linear programming formulations for TAP. Expand

An Improved Approximation Algorithm for the Matching Augmentation Problem

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We present a $\frac53$-approximation algorithm for the matching augmentation problem (MAP): given a multi-graph with edges of cost either zero or one such that the edges of cost zero form a matching,… Expand

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The first fast distributed approximations for weighted TAP are presented, and an O ( D )-round 2-approximation algorithm for the minimum size 2-edge-connected spanning subgraph is presented, which significantly improves upon the running time of previous approximation algorithms. Expand

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