Degree Type


Date of Award


Degree Name

Doctor of Philosophy


Electrical and Computer Engineering


Computer Engineering

First Advisor

Chris C. Chu


In integrated circuit design gate sizing is one of the key optimization techniques which is repeatedly invoked to trade-off delays for area and/or power of the gates during logic design and physical design stages. With increasing design sizes of a million gates and larger, discrete gate sizes and non-convex delay models the gate sizing algorithms that were designed for continuous sizes and convex delay models are slow and timing inaccurate.

Of the several published discrete gate sizing algorithms, recent works have shown that Lagrangian relaxation based gate sizers have produced designs with the lowest power on average with high timing accuracy. But they are also very slow due to a large number of expensive timing updates spread across hundreds of iterations of solving the Lagrangian sub-problem.

In this thesis we present a Lagrangian relaxation based multi-threaded discrete gate sizer for fast timing and power reduction by swapping the gate sizes and the threshold voltages. We developed two parallelization enabling techniques to reduce the runtime of Lagrangian sub-problem solver, namely, mutual exclusion edge (MEE) assignment and directed acyclic graph (DAG) based netlist traversal. MEEs are dummy edges assigned to reduce computational dependencies among gates sharing one or more common fan-ins. DAG based netlist traversal facilitates simultaneous resizing of gates belonging to different topological levels.

We designed a Lagrange multiplier update framework that enables rapid convergence of the timing recovery and power recovery algorithms. To reduce the runtime of timing updates, we proposed a simple and fast-to-compute effective capacitance model and several mechanisms to calibrate the timing models to improve their accuracy. Compared to the state-of-the-art gate sizer, our proposed gate sizer is on average 15x faster and the optimized designs have only 1.7\% higher power.

In digital synchronous designs simultaneous gate sizing and clock skew scheduling provides significantly more power saving. We extend the gate sizer to simultaneously schedule the clock skew. It can achieve an average of 18.8\% more reduction in power with only 20\% increase in the runtime.

Copyright Owner

Ankur Sharma



File Format


File Size

123 pages