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Directed self-assembly (DSA) is one of the leading candidates for extending the resolution of optical lithography to sub-7nm and beyond. By incorporating DSA in multiple patterning lithography (DSA-MP), the flexibility and resolution of contact/via patterning can be further enhanced by using multiple block copolymer (BCP) materials. Prior work faces the dilemma between solution quality and efficiency and is unable to handle 2D templates. In this paper, we capture the essence of template and mask assignment in DSA-MP by a new graph model and a new problem reduction: Our graph model explicitly represents spacing conflict edges and template hyperedges; thus, extra enumeration and manipulation of incompatible via grouping edges can be avoided, and arbitrary 1D/2D templates can be natively handled. We further reduce the assignment problem to exact cover, which is encoded by a sparse matrix. Our concise integer linear programming (ILP) formulation and fast backtracking heuristic achieve substantially superior solution quality and efficiency to the state-of-the-art work. Moreover, our method is flexible and extendible to utilize dummy vias to improve manufacturability. [ABSTRACT FROM AUTHOR]