Question: How do online stores select which products to show you? Answer: Algorithms!
This past summer, Taylor Kessler Faulkner '16 and Will Brackenbury '15 worked with Dr. Ashwin Lall to design algorithms for computing representative databases. The goal of the work was to design algorithms to prune down a large number of options to a smaller, representative set. The algorithm had to guarantee that any individual's best option in the full set, regardless of his or her utility function, is similar to one of the members of the smaller set. Such an algorithm would allow online stores to show customers a few appealing options rather than their entire inventory.
Taylor and Will were able to generalize some work of Dr. Lall and his co-authors from the case of linear utility functions to that of almost any concave or convex utility function. This is quite an improvement over the original work and a significant breakthrough. A paper on this work has been submitted for peer review at a prestigious database conference.