Open Problems These are open problems that I've encountered in the course of my research. Not surprisingly, almost all the problems are geometric in nature. A name in brackets is the first person to describe the problem to me; this may not be original source of the problem. If there's no name, either I thought of the problem myself (although I was certainly not the first to do so), or I just ...

Open Problems Antipodes. Jim Propp asks whether the two farthest apart points, as measured by surface distance, on a symmetric convex body must be opposite each other on the body. Apparently this is open even for rectangular boxes. Bounded degree triangulation. Pankaj Agarwal and Sandeep Sen ask for triangulations of convex polytopes in which the vertex or edge degree is bounded by a constant or ...

Ganley.org - The Steiner Tree Page - Open Problems Open Problems Of course, there are probably about a zillion open problems related to Steiner trees, but here are a few I've thought about. Please email me others if you like, and I'll include them here. Full trees. Hwang's theorem allows us to construct an optimal rectilinear Steiner tree of a full set in linear time. I know of no other metric ...