Although Self-Aligned Double and Quadruple Patterning (SADP, SAQP) have become the most promising processes for sub-20 nm and sub-14 nm node advanced technologies, not all wafer images are realized by them. In advanced technologies, feasible wafer images should be generated effectively by utilizing SADP and SAQP where a wafer image is uniquely determined by a selected mandrel pattern. However, predicting the wafer image of a mandrel pattern is not easy. In this paper, we propose a routing method of generating a feasible wafer image satisfying the connection requirements. Routing algorithms comprising simple connecting and cutting rules are performed on a new grid structure where two (SADP) or three colors (SAQP) are assigned alternately to grid-nodes. Then a mandrel pattern is selected without complex coloring or decomposition methods. Also, hotspot reduction by dummy pattern flipping is proposed. In experiments, feasible wafer images meeting the connection requirements are generated and the effectiveness of the proposed framework is confirmed.