Design automation algorithms: Research and applications

In the last few years there has been a great deal of basic research into computational complexity. This research has focused on the discovery of efficient algorithms for a wide range of problems. These problems include ones from number theory, geometry, graph theory, combinatorics, organizational research, and many other areas. Major progress has been made in both finding new fast and efficient algorithms and in showing for certain problems that no such algorithms can exist. Simultaneously, there has been a tremendous growth in VLSI technologies. Moreover, the design automation techniques needed to exploit this growth require very efficient algorithms. This is especially important as the density of chips continues to increase. For example, for each two-fold increase in chip density, a design algorithm that runs in n3 steps on a chip with n transistors requires a machine that is eight times faster - just to keep the design time constant per transistor.