The notion of polygon monotonicity has been well researched to be used as an important property for various geometric problems. This notion can be more extended for categorizing the boundary shapes of polyhedrons, but it has not been explored enough yet. This paper characterizes three types of polyhedron monotonicity: strong-, weak-, and directional-monotonicity: (Toussaint, 1985). We reexamine...

We consider polyhedral versions of Kannan and Lipton's Orbit Problem [14, 13] determining whether a target polyhedron V may be reached from a starting point x under repeated applications of a linear transformation A in an ambient vector space Q. In the context of program veri cation, very similar reachability questions were also considered and left open by Lee and Yannakakis in [15], and by Bra...

The cut polyhedron cut(G) of an undirected graph G = (V,E) is the dominant of the convex hull of all its nonempty edge cutsets. After examining various compact extended formulations for cut(G), we study some of its polyhedral properties. In particular, we characterize all the facets induced by inequalities with right-hand side at most 2. These include all the rank facets of the polyhedron.

Sanjeeb Dash IBM Research Ricardo Fukasawa Georgia Inst. Tech. Oktay G unl uk IBM Research March 6, 2008 Abstract We study the Master Equality Polyhedron (MEP) which generalizes the Master Cyclic Group Polyhedron and the Master Knapsack Polyhedron. We present an explicit characterization of the polar of the nontrivial facet-de ning inequalities for MEP. This result generalizes similar results...

Consider an orthogonal polyhedron, i.e., a polyhedron where (at least after a suitable rotation) all faces are perpendicular to a coordinate axis, and hence all edges are parallel to a coordinate axis. Clearly, any facial angle (i.e., the angle of a face at an incident vertex) is a multiple of π/2. Also, any dihedral angle (i.e., the angle between two planes that support to faces with a common ...

Corner Polyhedra were introduced by Gomory in the early 60s and were studied by Gomory and Johnson. The importance of the corner polyhedron is underscored by the fact that almost all “generic” cutting planes, both in the theoretical literature as well as ones used in practice, are valid for the corner polyhedron. So the corner polyhedron can be viewed as a unifying structure from which many of ...

The purpose of this article is to extract geometric features and other information for polyhedron, then using these features and information to build the model of object. In this essay, polyhedron refers to objects such as buildings. Unlike modelling objects in other fields, like reverse engineering, buildings’ surface usually consists of large amount of big and plane surfaces. Among these surf...

In this paper, we present a combinatorial theorem on a bounded polyhedron for an unrestricted integer labelling of a triangulation of the polyhedron, which can be interpreted as an extension of the Generalized Sperner lemma. When the labelling function is dual-proper, this theorem specializes to a second theorem on the polyhedron,-that is an extension of Scarf's dual Sperner lemma. These result...

We consider an oscillatory integral operator with Loomis—Whitney multilinear form. The phase is real analytic in a neighborhood of the origin ℝd and satisfies nondegeneracy condition related to its Newton polyhedron. Maximal decay obtained for this certain cases, depending on polyhedron given Lebesgue exponents. Our estimates imply volumes sublevel sets such functions are small relative product...