Vertex-Rounding a Three-Dimensional Polyhedral Subdivision

Vertex-Rounding a Three-Dimensional Polyhedral Subdivision

Morphing Three Dimensional Polyhedral Objects

On the refinements of a polyhedral subdivision

Let π:P→Q be an affine projection map between two polytopesP and Q. Billera and Sturmfels introduced in 1992 the concept of polyhedral subdivisions of Q induced by π (or π-induced) and the fiber polytope of the projection: a polytope Σ(P,π) of dimension dim(P )−dim(Q) whose faces are in correspondence with the coherent π-induced subdivisions (or π-coherent subdivisions). In this paper we invest...

On the Reenements of a Polyhedral Subdivision

Let : P ! Q be an aane projection map between two polytopes P and Q. Billera and Sturmfels introduced in 1992 the concept of polyhedral subdivisions of Q induced by (or-induced) and the ber polytope of the projection: a polytope (P;) of dimension dim(P) ? dim(Q) whose faces are in correspondence with the coherent-induced subdivisions (or-coherent subdivisions). In this paper we investigate the ...

Vertex sparsification and universal rounding algorithms

Suppose we are given a gigantic communication network, but are only interested in a small number of nodes (clients). There are many routing problems we could be asked to solve for our clients. Is there a much smaller network that we could write down on a sheet of paper and put in our pocket that approximately preserves all the relevant communication properties of the original network? As we wil...