Heterogeneous B∗-trees for analog placement with symmetry and regularity considerations

Symmetry constraints and regular structures are two major considerations for expert analog layout designers. Symmetry constraints are specified to place matched modules symmetrically with respect to some common axes to reduce unwanted electrical effects. Regular structures are commonly followed by experienced designers to enhance routability and suppress parasitics induced by extra bends of wires and via cost. In this paper, we propose a heterogeneous B*-tree representation to consider symmetry and regularity simultaneously. Corresponding moves and a new regularity cost modelling for the representation are also presented. Experimental results show that our approach can efficiently generate regularly structured placement satisfying all symmetry constraints. For example, our placer achieves a 18X runtime speedup, 28% smaller area, and 68% shorter wirelength than the previous work, based on placement results, and 60% fewer overflows, 39% fewer vias, and 86% shorter routed wirelength, based on global routing results.