Using a multiple storage quad tree on a hierarchical VLSI compaction scheme

A graph-generating algorithm and the experimental results of a hierarchical mask-layout-compaction scheme based on a plane-sweep algorithm, a fast region-query and a space-efficient data structure called the hierarchical multiple-storage quad tree are presented. For a mask-layout design, a rectangle is used as the primary element of the layout. Hence, in the hierarchical mask-compaction scheme, the graph-generating algorithm is based on the edges of rectangles rather than the central lines of symbols for the symbolic-compaction design. The plane-sweep algorithm is also called a dynamic event scheduling algorithm and can be applied to solve some other problems in the field of computational geometry and image processing. The efficiencies of the plane-sweep algorithm and the graph-generating algorithm are dependent on the region-query operations of the spatial data structure. By using the improved multiple storage quad tree as the spatial data structure in the system, the mask-layout compactor has been accomplished in a practically linear time performance in terms of the rectangles in the source layout