Advanced lithography techniques enable higher pattern resolution; however, techniques such as extreme ultraviolet lithography and e-beam lithography (EBL) are not yet ready for high volume production. Recently, complementary lithography has become promising, which allows two different lithography processes work together to achieve high quality layout patterns while not increasing much manufacturing cost. In this paper, we present a new layout decomposition framework for self-aligned double patterning and complementary EBL, which considers overlay minimization and EBL throughput optimization simultaneously. We perform conflict elimination by merge-and-cut technique and formulate it as a matching-based problem. The results show that our approach is fast and effective, where all conflicts are solved with minimal overlay error and e-beam utilization.