We describe a polynomial time algorithm that takes as input a polygon with axis-parallel sides but irrational vertex coordinates, and outputs a set of as few rectangles as possible into which it can be dissected by axis-parallel cuts and translations. The number of rectangles is the rank of the Dehn invariant of the polygon. The same method can also be used to dissect an axis-parallel polygon into a simple polygon with the minimum possible number of edges. When rotations or reflections are allowed, we can approximate the minimum number of rectangles to within a factor of two.

翻译：我们描述了一个多项式时间算法，该算法以具有轴平行边但顶点坐标为无理数的多边形为输入，输出一组尽可能少的矩形，使得该多边形可通过轴平行切割和平移剖分为这些矩形。矩形的数量等于该多边形Dehn不变量的秩。同一方法还可用于将轴平行多边形剖分为边数尽可能少的简单多边形。当允许旋转或反射时，我们能在两倍因子内逼近所需矩形的最小数量。