The definition of the Manhattan geometry is adopted from Ref. . The a pattern has a Manhattan geometry, if at least one partition of the pattern includes a set of objects satisfying the following conditions: First, all objects are rectangles, and any two rectangles that share an entire edge are merged and considered as a single rectangular object. Second, all edges of objects have either vertical or horizontal orientation. Third, all edges have length , where is the minimum feature size of the pattern. A typical Manhattan geometry pattern is illustrated in Fig. B.1.