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

  title={Approximating (Unweighted) Tree Augmentation via Lift-and-Project, Part II},
  author={J. Cheriyan and Zhihan Gao},
  • J. Cheriyan, Zhihan Gao
  • Published 2017
  • Mathematics, Computer Science
  • Algorithmica
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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