References:
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Ajit Agrawal, Philip N. Klein, R. Ravi, "When Trees Collide: An
Approximation Algorithm for the Generalized Steiner Problem on
Networks," SIAM J. Comput. 24(3): 440-456 (1995)

Gives the original moat-growing 2-approximation algorithm for Steiner
tree.

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Michel X. Goemans, David P. Williamson, "A General Approximation
Technique for Constrained Forest Problems," SIAM J. Comput. 24(2):
296-317 (1995)

Generalizes the AKR algorithm and casts it in the terms I presented in
my lecture.  This is paper also gave the algorithm for
prize-collecting Steiner tree.

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Naveen Garg, "A 3-Approximation for the Minimum Tree Spanning k
Vertices," FOCS 1996: 302-309

Fabian A. Chudak, Tim Roughgarden, David P. Williamson, "Approximate
k-MSTs and k-Steiner trees via the primal-dual method and Lagrangean
relaxation," Math. Program. 100(2): 411-421 (2004)

Naveen Garg, "Saving an epsilon: a 2-approximation for the k-MST
problem in graphs," STOC 2005: 396-402

The CRW paper re-interprets Garg's FOCS '96 paper in terms of
Lagrangian relaxation, as I presented in the lecture.  This view is
also helpful in interpreting Garg's later STOC '05 paper.

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Aaron Archer, Asaf Levin, David P. Williamson,
"A Faster, Better Approximation Algorithm for the Minimum Latency
Problem," SIAM J. Comput. 37(5): 1472-1498 (2008)

My viewpoint is obviously biased, but I think this is the best
reference to help one gain a visceral understanding of how Lagrangian
relaxation has been used to design approximation algorithms.