The sequence-pair was proposed as a representation method of block placement to determine the densest possible placement of rectangular modules in VLSI layout design. A method of achieving bottom left corner packing in O(n2) time based on a given sequence-pair of n rectangles was proposed using horizontal/vertical constraint graphs. Also, a method of determining packing from a sequence-pair in O(n log n) time was proposed. Another method of obtaining packing in O(n log log n) time was recently proposed, but further improvement was still required. In this paper, we propose a method of obtaining packing via the Q-sequence (representation of rectangular dissection) in O(n+k) time from a given sequence-pair of n rectangles with k subsequences called adjacent crosses, given the position of adjacent crosses and the insertion order of dummy modules into adjacent crosses. The position of adjacent crosses and insertion order of dummy modules can be obtained from a sequence-pair in O(n+k) time using the conventional method. Here, we prove that arbitrary packing can be represented by a sequence-pair, keeping the value of k not more than n-3. Therefore, we can determine packing from a sequence-pair with k of O(n) in linear time using the proposed method and the conventional method.

With being pushed into sub-16nm regime, advanced technology nodes printing in optical micro-lithography relies heavily on aggressive Optical Proximity Correction (OPC) in the foreseeable future. Although acceptable pattern fidelity is utilized under process variations, mask design time and mask manufacturability form crucial parameters whose tackling in the OPC recipe is highly demanded by the industry. In this paper, we propose an intensity based OPC algorithm to find a highly manufacturable mask solution for a target pattern with acceptable pattern fidelity under process variations within a short computation time. This is achieved through utilizing a fast intensity estimation model in which intensity is numerically correlated with local mask density and kernel type to estimate the intensity in a short time and with acceptable estimation accuracy. This estimated intensity is used to guide feature shifting, alignment, and concatenation following linearly interpolated variational intensity error model to achieve high mask manufacturability with preserving acceptable pattern fidelity under process variations. Experimental results show the effectiveness of our proposed algorithm on the public benchmarks.

This paper discusses how to minimize the number of dissection lines regarded as wiring channels on a floorplan corresponding to a placement of n modules. In a floorplan (rectangular dissection), the number of dissection lines exceeds the number of rooms exactly by three. Since a floorplan obtained from a given module placement may have many empty rooms where no module is assigned, redundant wiring channels and wire bends may also be generated. Hence, in order to reduce redundant channels and wire bends, removal of empty rooms is required. For this purpose, we formulate a problem of obtaining a floorplan with the minimum possible empty rooms based on a given module placement. Then, we propose a method of removing as many redundant empty rooms as possible by merging dissection lines on a floorplan in O(n) time. The number of empty rooms in the resultant floorplan is reduced to n- or less.

A 3D-dissection (A rectangular solid dissection) is a dissection of a rectangular solid into smaller rectangular solids by planes. In this paper, we propose an O-sequence, a string of representing any 3D-dissection which is dissected by only non-crossing rectangular planes. We also present a necessary and sufficient condition for a given string to be an O-sequence.

In the VLSI layout design, a floorplan is often obtained to define rough arrangement of modules in the early design stage. In the stage, the aspect ratio of each soft module is also determined. The aspect ratio can be changed in the designated range keeping its area of each module. In this paper, in order to determine the aspect ratio, we propose a graph-based one dimensional compaction method which determines the aspect ratio quickly under the constraint that topology of a floorplan must not be changed. The proposed method is divided into two steps: (1) Selection of a minimal set of soft modules to adjust the aspect ratio. (2) Decision on the aspect ratio. (1) is formulated as the minimal cut problem in graph theory. We solve the problem by transforming it to the shortest path problem. (2) is divided into two operations. One is to determine the increment limit in height or width of each soft module and the other is to determine the aspect ratio of each soft module by Newton-Raphson method. The experimental comparisons show effectiveness of the proposed method.

In this paper, for convex rectilinear block packing problem, we propose 1) a novel algorithm to obtain a packing based on a given sequence-pair in O(n2) time (conventional method needs O(n3) time), where n is the number of rectangle sub-blocks made from convex blocks, 2) a move operation for Simulated Annealing which is symmetric and can guarantee reachability for the first time, and 3) a method to generate a random adjacent sequence-pair in O(n2) time. By using 1), 2) and 3) together, the time complexity of the inner loop in Simulated Annealing becomes surely O(n2) time. Experimental results show that the proposed algorithm is faster than the conventional ones in practical and the wire length as well as packing area is taken into consideration in the proposed method.

Self-Aligned Quadruple Patterning (SAQP) is an important manufacturing technique for sub 14nm technology node. Although various routing algorithms for SAQP have been proposed, it is not easy to find a dense SAQP compliant routing pattern efficiently. Even though a grid for SAQP compliant routing pattern was proposed, it is not easy to find a valid routing pattern on the grid. The routing pattern of SAQP on the grid consists of three types of routing. Among them, third type has turn prohibition constraint on the grid. Typical routing algorithms often fail to find a valid routing for third type. In this paper, a simple directed grid-graph for third type is proposed. Valid SAQP compliant two dimensional routing patterns are found effectively by utilizing the proposed directed grid-graph. Experiments show that SAQP compliant routing patterns are found efficiently by our proposed method.