How to merge images compactly?

Question

Image processing

You need a service, a program or a script, for example for python, to compactly compose collages from images. It is required to compose a collage without resizing the original images, but rather with the control of this parameter, in automatic mode and the possibility of manual editing.
What is needed is not beautiful effects, but automatic calculation and placement of images, taking into account their size.
arrange pictures by analogy.

Answer 1

The optimization problem (pack N rectangles into the minimum area) is a special case of the packing algorithm (be sure to read the Wikipedia article).
Here I found a resource (in English, though), several algorithms are described there:
cgi.csc.liv.ac.uk/~epa/surveyhtml.html
Here's another one: Cutting task

Answer 2

Made square previews with ImageMagick. If you dig, you can glue it with different rectangles.