Supporting VLSI geometry operations in a database system

VLSI layout systems perform various operations on design data describing the layouts of geometries (rectangles) on different mask layers. In this paper, we identify a basic set of such operations and show a formulation of these operations in terms of expressions of predicates that are suitable for processing by a database system. We then describe the operations and properties of a 4-D (four-dimensional) tree structure for efficiently supporting these operations. We also provide a qualitative analysis of the time complexity of the data structure, which compares favorably against various existing proposals.