1 research outputs found
A lower bound technique for triangulations of simplotopes
Products of simplices, called simplotopes, and their triangulations arise
naturally in algorithmic applications in game theory and optimization. We
develop techniques to derive lower bounds for the size of simplicial covers and
triangulations of simplotopes, including those with interior vertices. We
establish that a minimal triangulation of a product of two simplices is given
by a vertex triangulation, i.e., one without interior vertices. For products of
more than two simplices, we produce bounds for products of segments and
triangles. Aside from cubes, these are the first known lower bounds for
triangulations of simplotopes with three or more factors, and our techniques
suggest extensions to products of other kinds of simplices. We also construct a
minimal triangulation of size 10 for the product of a triangle and a square
using our lower bound.Comment: 31 pages, related work at http://www.math.hmc.edu/~su/papers.htm