GORDIAN: VLSI Placement by Quadratic Programming and Slicing Optimization

In this paper we present a new placement method for cell-based layout styles. It is composed of alternating and interacting global optimization and partitioning steps that are followed by an optimization of the area utilizaiton. Methods using the divide-and-conquer paradigm usually lose the global view by generating smaller and smaller subproblems. In contrast, GORDIAN maintains the simultaneous treatment of all cells over all global optimization steps, thereby considering constraints that reflect the current dissection of the circuit. The global optimizations are performed by solving quadratic programming problems that possess unique global minima. Improved partitioning schemes for the stepwise refinement of the placement are introduced. The area utilization is optimized by an exhaustive slicing procedure. The placement method has been applied to real world problems and excellent results in terms of both placement quality and computation time have been obtained.