This research is an investigation into fundamental aspects of computer-aided design of VLSI circuits. Topics include high level synthesis, logic synthesis and physical design, with an emphasis on the application of modern combinatorial optimization technique for the solution of complex design automation problems The research has two orthogonal themes, one in low power design in high level and logic synthesis, and the other in algorithmic approaches to physical design problems. The second theme is computational technique oriented, showing how techniques such as linear, integer and convex programming and network flow can be applied to the solution of design automation problems.