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While the next generation of lithography systems is still under development, extending optical lithography using double patterning (DP) is the only solution to continue technology scaling. The biggest technical challenge of DP is the presence of mask-assignment conflicts in dense layers. In this paper, we propose a framework for DP conflict removal for standard cells. First, we offer an O(n) algorithm for mask assignment (up to 200× faster than the ILP-based approach) that guarantees a conflict-free solution if one exists. We then formulate the problem of conflict removal as a linear program (LP), which permits an extremely fast run-time (less than 10 seconds in real time for typical cells). The framework removes DP conflicts and legalizes the layout across all layers simultaneously while minimizing layout perturbation. For cells from a commercial 22nm library designed without any DP awareness, our method usually removes all DP conflicts without any area increase; for some complex cells, the method still removes all conflicts with a modest 6.7% average increase in area. The method is more general, however, and can also be applied for macro layouts and the interconnect layers in complete designs as we demonstrate in the paper.