My favorite reference for linear programming is the book
Introduction to Linear Optimization by Bertsimas and Tsitsiklis. The ellipsoid method in all its gory details is given in
this book, but I don't recommend it as bedside reading. The facility location algorithm done today is due to
Shmoys, Tardos, and Aardal , and is the first constant factor approximation for it. The algorithm for generalized assignment problem (GAP) we did in class is due to
Shmoys and Tardos , although they
look at a minimization problem; the fact that this implies 2-approximation for the maximization version, the part which we couldn't complete due to the fire, is due to
Chekuri and Khanna .