Find set of non-overlapping rectangles in a 2D grid
The problem you state is shown to be NP-Hard [1, 2]. However, there is an $O(\log \log n)$ approximation algorithm for the problem [3]. 

[1] H. Imai, T. Asano. Finding the Connected Components and a Maximum Clique of an Intersection Graph of Rectangles in the Plane. Journal of Algorithms 4(4): 310-323, 1983.

[2] R.J. Fowler, M.S. Paterson and S.L. Tanimoto, Optimal packing and covering in the plane are NPcomplete. Information Processing Letter. 12 3 (1981), pp. 133137.

[3] Parinya Chalermsook, Julia Chuzhoy: Maximum independent set of rectangles. SODA 2009: 892-901