Variability inspired implementation selection problem

Given a directed acyclic graph and different possible implementations for each node, the implementation selection problem (ISP) selects the appropriate implementation for each node such that a given global design objective is optimized, ISP is a generic formulation that is explicitly or implicitly solved in several design automation problems like leakage optimization using dual V_th, gate sizing, etc. An implementation of a node results in an associated delay and perhaps cost for the node. In the presence of different sources of uncertainty and fabrication variability, fixed estimates of delays and costs of a node are extremely erroneous. We investigate a probabilistic approach to solve ISP by considering probability density functions for delays and costs of a node. We propose a dynamic-programming based approach in a probabilistic sense and introduce effective pruning criteria when dealing with probability distributions for identifying co-optimal solution at each stage. A case study of leakage optimization using dual V_th is presented where we show the effectiveness of a probabilistic approach considering V_th variability over a traditional deterministic one.