A K-hedral tiling of a 2D finite domain is a covering of the domain with tiles without gaps or overlaps, where each tile is congruent to one of the K distinct shapes called prototiles. K, the number of prototiles, is preferred to be as small as possible for congruent tiling appearance and reducing fabrication cost, e.g., by molding. Typically, a forward approach is adopted to produce K-hedral tilings by prescribing a set of prototiles and placing prototile instances (i.e., tiles) to cover the input domain. However, the prescribed prototile set may not be sufficient to tile the domain (for small K) or may lead to tiling results with excessive prototiles more than needed (for large K).