Novel Convex Optimization Approaches for VLSI Floorplanning
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The floorplanning problem aims to arrange a set of rectangular modules on a rectangular chip area so as to optimize an appropriate measure of performance. This problem is known to be NP-hard, and is particularly challenging if the chip dimensions are fixed. Fixed-outline floorplanning is becoming increasingly important as a tool to design flows in the hierarchical design of Application Specific Integrated Circuits and System-On-Chip. Therefore, it has recently received much attention. A two-stage convex optimization methodology is proposed to solve the fixed-outline floorplanning problem. It is a global optimization problem for wirelength minimization. In the first stage, an attractor-repeller convex optimization model provides the relative positions of the modules on the floorplan. The second stage places and sizes the modules using convex optimization. Given the relative positions of the modules from the first stage, a Voronoi diagram and Delaunay triangulation method is used to obtain a planar graph and hence a relative position matrix connecting the two stages. An efficient method for generating sparse relative position matrices and an interchange-free algorithm for local improvement of the floorplan are also presented. Experimental results on the standard benchmarks MCNC and GSRC demonstrate that we obtain significant improvements on the best results in the literature. Overlap-free and deadspace-free floorplans are achieved in a fixed outline and floorplans with any specified percentage of whitespace can be produced. Most important, our method provides a greater improvement as the number of modules increases. A very important feature of our methodology is that not only do the dimensions of the floorplans in our experiments comply with the original ones provided in the GSRC benchmark, but also zero-deadspace floorplans can be obtained. Thus, our approach is able to guarantee complete area utilization in a fixed-outline situation. Our method is also applicable to area minimization in classical floorplanning.