My current research project involves a large scale computation and classification of knot diagrams.
Until now, computer tabulations have begun by first reducing the (giant) set of all link diagrams, often through highly clever means; then they proceed to test whether links are equivalent. Our project, the Census of Link Diagrams (COLD), creates a database of all link diagrams, up to a certain crossing number. From there, we reduce to a complete tabulation of both prime and composite links. The first goal of the project is to tabulate the complete set of link diagrams through 9 crossings. We then classify the knot types of the diagrams using a Map Reduce algorithm. This project is joint with Jason Cantarella at the University of Georgia and Jason Parsley at Wake Forest University.
For more information you can take a look at this talk that I gave at Tulane University in Spring 2015.