Multi-Sweep-Line Algorithm for Rectangle Union on GPU and Its Application for VLSI Density Calculation

Graphics Processing Units (GPUs) have been widely used for computational intensive applications owing to its massive number of computing cores. However, only few algorithms can fully utilize the computational power of GPUs, because it requires not only enough degree of parallelism, but also the synergetic control between computation and data access in the finest granularity. In this paper, we proposed the Multi-Sweep-Line (MSL) algorithm on GPU for VLSI layout density calculation, which computes the union area of components in a layout. The shapes of most components are rectilinear rectangles. The MSL algorithm divides the input layout hierarchically into windows, slabs, and sweep line regions to explore the large degree of parallelism. In addition, to overcome the memory pressure of GPU, tasks are partitioned into batches based on the estimated memory usage. Optimization techniques, including fast segmented sort, reducing atomic instruction, and load balance, are also applied to further improve the performance. The experimental results show that our MSL implementation can achieve 75 to 160 times speedup over the CPU version using one Nvidia GTX 1080TI.

I. Introduction

In Very Large Scale Integration (VLSI) design, metal and pattern density check, which calculates polygons union area, is required to ensure the mechanical sturdiness of the chip as a whole and to achieve a smooth planar structure for different metal layers, so that all metal layers are uniform in structure and performance. If the metal density is not uniform distributed, some metal layers may be more in height than others and hence the timing, EM, power integrity may be affected. There are some libraries, like Boost, providing sequence polygon union function.