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Multiple patterning lithography has been recognized as one of the most promising solutions, in addition to extreme ultraviolet lithography, directed self-assembly, nanoimprint lithography, and electron beam lithography, for advancing the resolution limit of conventional optical lithography. Multiple patterning layout decomposition (MPLD) becomes more challenging as advanced technology introduces complex coloring rules. Existing works model MPLD as a graph coloring problem; nevertheless, when complex coloring rules are considered, layout decomposition can no longer be modeled accurately by graph coloring. Therefore, in this paper, for capturing the essence of layout decomposition with complex coloring rules, we model the MPLD problem as an exact cover problem. We then propose a fast and exact MPLD framework based on augmented dancing links. Our method is flexible and general: it can consider the basic and complex coloring rules simultaneously, can maintain density balancing, and can handle quadruple patterning and beyond. Experimental results show that our approach outperforms state-of-the-art works on reported conflicts and stitches and is promising for handling complex coloring rules and density balancing as well.

Irregular subarray technology is presented in this paper for wide-angle scanning phased arrays. Based on the exact set cover theory and dancing links algorithm, a solution of the exact partition is developed using different kinds of irregular subarrays. Simulation results show that the irregular subarray architecture exhibits good radiation performances as well as no-sub array architecture.

Exact cover problem is a well-known NP-complete decision problem to determine if the exact cover really exists. In this paper, we show how to solve a modified version of the famous Hexomino puzzle (being a noteworthy example of an exact cover problem) using a Dancing-links based algorithm. In this modified problem, a limited number of gaps in the rectangular box may be left uncovered (this is a common scenario in a variety of spatial planning problems). Additionally, we present the benchmark generator which allows for elaborating very demanding yet solvable problem instances. These instances were used during the qualifying round of Deadline24—an international 24-h programming marathon. Finally, we confront our baseline solutions with those submitted by the contestants, and elaborated using our two solvers.

Multiple patterning lithography has been recognized as one of the most promising solutions, in addition to extreme ultraviolet lithography, directed self-assembly, nanoimprint lithography, and electron beam lithography, for advancing the resolution limit of conventional optical lithography. Multiple patterning layout decomposition (MPLD) becomes more challenging as advanced technology introduces complex coloring rules. Existing works model MPLD as a graph coloring problem; nevertheless, when complex coloring rules are considered, layout decomposition can no longer be modeled accurately by graph coloring. Therefore, in this paper, for capturing the essence of layout decomposition with complex coloring rules, we model the MPLD problem as an exact cover problem. We then propose a fast and exact MPLD framework based on augmented dancing links. Our method is flexible and general: It can consider the basic and complex coloring rules simultaneously, and it can handle quadruple patterning and beyond. Experimental results show that our approach outperforms state-of-the-art works on reported conflicts and stitches and is promising for handling complex coloring rules as well.

The N-Queens problem has been studied for over a century. The N-Queens problem may be solved using a variety of methods including backtracking algorithms and mathematical equations such as magic squares. We propose a more efficient approach to the most used technique, backtracking, by removing the threatened cells in order to decrease the number of trial and error steps.