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Double patterning technology (DPT) is regarded as the most practical solution for the sub-22nm lithography technology. DPT decomposes a single layout into two masks and applies double exposure to print the shapes in the layout. DPT requires accurate overlay control. Thus, the primary objective in DPT decomposition is to minimize the number of stitches (overlay) between the shapes in the two masks. The problem of minimizing the number of stitches in DPT decomposition is conjectured to be NP-hard. Existing approaches either apply Integer Linear Programming (ILP) or use heuristics. In this paper, we show that the problem is actually in P and present a method to decompose a layout for DPT and minimize the number of stitches optimally. The complexity of the method is O(n1.5 log n). Experimental results show that the method is even faster than the fast heuristics.