random placement of rectangles with no overlaps

Question

I am looking for a sound algorithm that would randomly place a given number of rectangles of the same size into a bigger rectangle (canvas).

I see two ways to do it:

Answer 1

Here is a simple heuristic. It will be non-overlapping and random.

Place a rectangle randomly. Then, calculate the intersections of extensions of the the two parallel edges of the first rectangle with the edges of the canvas. You will obtain four convex empty regions. Place other rectangles in these empty regions one-by-one independently and calculate the similar divisions for placements. And try to put the remaining rectangles in empty regions.

You can try different strategies. You can try to place the rectangles close to the corners. Or, you can place them around the center of the regions. We cannot discuss optimality because you introduced randomness.