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Self-aligned multiple patterning, due to its low overlay error, has emerged as the leading option for 1-D gridded back-end-of-line (BEOL) in sub-14-nm nodes. To form actual routing patterns from a uniform “sea of wires,” cut masks are needed for line-end cutting or realization of space between routing segments. The line-end cutting results in nonfunctional (i.e., dummy fill) patterns that change wire capacitance, and hence design timing and power. Therefore, to remove such dummy fill patterns, extra 2-D block masks are used. However, 2-D block masks cannot remove arbitrary dummy fill patterns, due to design rule constraints on the block mask shapes. In this paper, we address the timing-aware optimization of 2-D block mask layouts under various sets of mask rules that are derived from mask patterning technology options (e.g., 193i and 193d) for foundry 7-/5-nm (N7/N5) BEOL. Our central contribution is a mixed integer linear programming (MILP) optimization that minimizes timing impact due to dummy metal segments while satisfying block mask rules and metal density constraints. We also propose a distributed optimization flow to improve the scalability. With our optimizer, we recover up to 84% of the worst negative slack impact from dummy segments, with up to 64% dummy removal rate. We further extend our MILP to a co-optimization of cut and block masks. This paper gives new insights into fundamental limits of benefit from emerging cut and block mask technology options. [ABSTRACT FROM AUTHOR]