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The problem of tiling a rectangle by polyominoes is known to be NP-complete if the polyominoes used are polylogarithmic in size. On the other hand, if the same is true for polyominoes of sub-logarithmic size, this would imply P=NP.This paper closes the gap between logarithmic and polylogarithmic-sized pieces by proving that tiling remains NP-complete even when only pieces of logarithmic area are used...
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