Mathematical Sciences Department Discrete Math Seminar
Nathaniel Itty, Blake Bruell, and Ryan Offstein, WPI
Monday, April 14th
3:00pm - 4:00 pm
Title: Slicing the Hypercube
Abstract: Our work sought to determine the minimum number of hyperplanes, S(n), required to slice all edges of an n-dimensional hypercube. A highly optimized Tabu search algorithm was implemented in Rust, leveraging low level optimizations, a novel geometric construction, the reduced hypercube, and clever heuristics, to explore trillions of solutions. We contribute new constructions matching or improving the best results in literature, notably a solution in 11 dimensions slicing 11,258 out of 11,264 edges, 6 edges short of improving a 50+ year old upper bound. Furthermore, we developed a tool allowing users to visualize the reduced hypercube and our new constructions.