Given a set of Squares $\mathcal{S}=\{w_1, w_2, \ldots, w_n\}$ and a rectangle $\mathcal{R}$ of dimensions $a\times b$. Is there a placement of the squares in $\mathcal{S}$ to cover $\mathcal{R}$.
The union of squares should include $\mathcal{R}$, i.e., we allow for overlapping and covering of regions that do not belong to $\mathcal{R}$.
We can consider the problem only allowing for translation, or also considering arbitrary rotation. What is the theoretical complexity of the problem(s)? (P or NP?)
[1] established NP-hardness for covering a rectangle using rectangles. But the reduction involves number -> rectangles, which does not trivially translate to squares.
I would be grateful for any references to papers, considering covering polygons, given a set of polygons. Anything would be helpful.
[1] Daniels, Karen & Milenkovic, Victor. (1997). Multiple Translational Containment Part I: An Approximate Algorithm. Algorithmica. 19. 148-182.