To further improve the resource efficiency of p-polyhedron protection scheme against multi-link failures in optical data center networks (ODCNs), content connectivity is considered when constructing structure. In this paper, connectivity-based polyhedron (CCPP) proposed. An ILP model and a heuristic algorithm are developed to realize CCPP scheme. Numerical results show that proposed has lower n...

We study a polyhedron with $n$ vertices of fixed volume having the minimum surface area. Completing proof Fejes Tóth, we show that all faces are triangles, and further prove does not allow deformation single vertex. also present possible shapes for $n ≤ 12$. Some them quite unexpected, in particular = 8$.

We study the relationship between the vertices of an up-monotone polyhedron and those of the polytope obtained by truncating it with the unit hypercube. When the original polyhedron has binary vertices, we characterize the vertices of the truncated polytope in terms of the original vertices, prove their integrality, and show the equivalence of adjacencies in either polyhedron. We conclude by ap...

Four decades ago, Gomory introduced the corner polyhedron as a relaxation of a mixed integer set in tableau form and Balas introduced intersection cuts for the corner polyhedron. A recent paper of Andersen, Louveaux, Weismantel and Wolsey has generated a renewed interest in the corner polyhedron and intersection cuts. We survey these two approaches and the recent developments in multi-row cuts....

A minimum tetrahedralization of a convex polyhedron is a partition of the convex polyhedron with minimum number of tetrahedra. The problem of finding the minimum tetrahedralization of a convex polyhedron is known to be NP-Hard. In this paper, a genetic algorithm is presented to find an approximate solution to this problem. Our result always shows improvements to those produced by commonly used ...

We show that every orthogonal polyhedron homeomorphic to a sphere can be unfolded without overlap while using only polynomially many (orthogonal) cuts. By contrast, the best previous such result used exponentially many cuts. More precisely, given an orthogonal polyhedron with n vertices, the algorithm cuts the polyhedron only where it is met by the grid of coordinate planes passing through the ...

Unrestricted control polyhedra facilitate modeling free-form surfaces of arbitrary topology and local patch-layout by allowing n-sided, possibly non-planar facets and m-valent vertices. By cutting oo edges and corners, the smoothing of an unrestricted control polyhedron can be reduced to the smoothing of a planar-cut polyhedron. A planar-cut polyhedron is a generalization of the well-known tens...