Algorithm for tiling an arbitrary set polyominoes is some finite space region?

Question

Does an efficient (i.e. P-complete) algorithm exist that can tile an arbitrary set of polyominoes, within a finite region? Could you point me to some websites that elaborate on the subject?

Searching on the web only returned results related to infinite spaces or repeated usage of a specific polyomino. I'm looking for one that can handle any set, using every element exactly once.

Thank you

(I'm interested in general algorithms. An arbitrary shaped space, translation and rotation only. But small variations on these requirements would be of interest to me as well)

Answer 1

Please take a look at the following Master's Thesis about algorithms for Treemaps with bounded aspect ratio.