TITLE: Algorithm for positioning rectangles of various size into a larger rectangle
QUESTION [6 upvotes]: I am working on tool for merging smaller textures into one larger for use on Android app.
I have $n$ rectangles of given size $(w_k, h_k)$, where $k=1,\ldots,n$ and I need to position them within master rectangle of size $2^l \times 2^m$, where $l, m \leq 9$ so none overlapping occur and $2^l \times 2^m$ has minimal possible value. The result should be $(x_k, y_k)$, a position of each of the $n$ base rectangles or information that such positioning is impossible.

REPLY [2 votes]: I guess this
 should be exactly what you need. Basically it is an implementation of the approach presented in this paper by Richard E. Korf.
To quote the introduction:

Given a set of rectangles with fixed orientations, we want to
  find an enclosing rectangle of minimum area that contains
  them all with no overlap. Many simple scheduling tasks can
  be modelled by this NP-complete problem. We use an anytime
  branch-and-bound algorithm to solve the problem optimally.