Multi-SP: a representation with united rectangles for analog placement and routing

In analog layout, the placement and routing are closely connected with each other in the optimization of the area, the parasitics, the mutability and so on. In this paper, we introduce a common data-structure to the placement and multilayer routing, where devices and wires are represented by united rectangles. It is called multi-layer sequence-pair (multi-SP). We also provide a bi-directional translation between a layout and a multi-SP under align-constraint. Since the multi-SP is geometry free, it enables us to manage diversified methodologies such as device sizing and technology migration. Also, it gives a way to take the parasitics between devices and wires of optimizing placement and routing simultaneously. We implemented a compaction tool based on multi-SP and showed its potential experimentally