  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 $\leq
\frac{3}{2}+\epsilon$, where $\epsilon>0$ can be any small constant. We obtain
this result by designing a polynomial-time algorithm for TAP that achieves an
approximation guarantee of ($\frac32+\epsilon$) relative to the SDP relaxation.
The algorithm is combinatorial and does not solve the SDP relaxation, but our
analysis relies on the SDP relaxation.
  We generalize the combinatorial analysis of integral solutions from the
previous literature to fractional solutions by identifying some properties of
fractional solutions of the Lasserre system via the decomposition result of
Karlin, Mathieu and Nguyen (IPCO 2011).
