Tiling with Squares and Packing Dominos in Polynomial Time

A polyomino is a polygonal region with axis-parallel edges and corners of integral coordinates, which may have holes. In this paper, we consider planar tiling packing problems pieces container P . We give polynomial-time algorithms for deciding if can be tiled k × squares any fixed part the input (that is, union set non-overlapping squares) maximum number 2 1 dominos, allowing rotations by 90°. As more general than tiling, latter algorithm also used to decide dominos. These are classical important applications in VLSI design, related problem finding known NP-hard [6]. For our three there pseudo-polynomial-time algorithms, that running times polynomial area or perimeter However, standard, compact way represent polygon listing coordinates binary. use representation, thus present first problems. Concretely, simple O ( n log )-time squares, where then involved reduces dominos perfect matching graph 3 ) vertices. This leads \(O({n^3 \frac{\log ^3 n}{\log ^2\log n} }) \) ^2 \log , respectively.