Asynchronous circuit placement by Lagrangian relaxation

Recent asynchronous VLSI circuit placement approach tries to leverage synchronous placement tools as much as possible by manual loop-breaking and creation of virtual clocks. However, this approach produces an exponential number of explicit timing constraints which is beyond the ability of synchronous placement tools to handle. Thus, synchronous placer can only produce suboptimal results. Also, it can be very costly in terms of runtime. This paper proposed a new placement approach for asynchronous VLSI circuits. We formulated the asynchronous timing-driven placement problem and transform this problem into a weighted wirelength minimization problem based on a Lagrangian relaxation framework. The problem can then be efficiently solved using any standard wirelength-driven placement engine that can handle net weights. We demonstrate our approach on QDI PCHB asynchronous circuit with a state-of-art quadratic placer. The experimental results show that our algorithm can effectively improve the asynchronous circuits performance at placement stage. In addition, the runtime of our algorithm is shown to be more scalable to large-scale circuits compared with the loop-breaking approach.