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Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 48 for “"polyhedron"”.
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Iterative Schedule Optimization for Parallelization in the Polyhedron Model
… for optimizing compilers. In this context, the polyhedron model is of help as it provides not only a mathematical representation of programs but, more importantly, a uniform representation of complex sequences of program transformations by schedule functions. The latter facilitates the …
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Code Optimization in the Polyhedron Model - Improving the Efficiency of Parallel Loop Nests
… basis for automatic loop parallelization is the polyhedron model which represents the iteration domain of a loop nest as a polyhedron in $\mathbb{Z}^n$. However, turning the parallel loop program in the model to efficient code meets with several obstacles, due to which performance may deteriorate …
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A pseudopolynomial algorithm for Alexandrov's theorem
… topology and local geometry required of a convex polyhedron is in fact the intrinsic metric of some convex polyhedron. Recent work by Bobenko and Izmestiev describes a differential equation whose solution is the polyhedron corresponding to a given metric. We describe an algorithm based on this …
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Flexible polyhedra - Exploring finite mechanisms of triangulated polyhedra
… whether each rotational position of a flexible polyhedron is physically possible; then a range of motion is defined between occurrences of clashes at the two ends; finally, an optimisation tool is used to maximise the range of motion. By using these tools, the range of motion of two types of …
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Boundaries of K-types in discrete series
… a set of lattice points in a noncompact convex polyhedron. In this paper we shall describe a recursive algorithm for finding the boundary facets of this polyhedron.
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Polyhedral Computation for Differential System Analysis and Control
… class of systems. However, finding a suitable polyhedron is a difficult problem. This is to a large extent inevitable, since many of the above problems are known to be computationally intractable. Despite this, the conditions that a polyhedron must satisfy in the above problems have a strong …
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On the matrix cuts of Lovasz and Schrijver and their use in integer programming
… to optimize) with the 0-1 vectors in a given polyhedron and to derive linear inequalities valid for these 0-1 vectors from a linear inequality system defining the polyhedron. Lovasz and Schrijver (1991) described a family of operators, called the matrix-cut operators, which generate strong …
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Closed quasigeodesics, escaping from polygons, and conflict-free graph coloring
… A closed quasigeodesic on the surface of a polyhedron is a loop which can everywhere locally be unfolded to a straight line: thus, it's straight on faces, uniquely determined on edges, and has as much flexibility at a vertex as that vertex's curvature. On any polyhedron, at least three …
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Kissing the Archimedeans
… of these outer spheres are the vertices of the polyhedron, and these outer spheres will continue to expand until they become tangent to each other. The ratio will be found between the radius of each outer sphere, and the radius of an inner sphere such that each inner sphere's center is the …
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Robust optimization, game theory, and variational inequalities
… variational inequality (VI) problem over a polyhedron, the finite game under payoff uncertainty, and the network design problem under demand uncertainty. In the first part of the thesis, we demonstrate that the nominal VI problem is in fact a special instance of a robust constraint. Using …
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Traveling salesman path problems
… linear programming, we study properties of the polyhedron corresponding to a linear programming relaxation of the traveling salesman walk problem. Our results relate the structure of the underlying graph of the problem instance with polyhedral properties of the corresponding fractional walk …
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Combinatorial optimization problems with concave costs
… minimizing a separable concave function over a polyhedron. We assume the concave functions are nonnegative nondecreasing on R+, and the polyhedron is in RI' (these assumptions can be relaxed further under suitable technical conditions). We show how to approximate this problem to 1+ E precision …
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The Gomory-Chvátal closure : polyhedrality, complexity, and extensions
… polyhedra. A Gomory-Chvátal cutting plane for a polyhedron P is derived from any rational inequality that is valid for P by shifting the boundary of the associated half-space towards the polyhedron until it intersects an integer point. The Gomory-ChvAital closure of P is the intersection of all …
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Data analysis to understand coordination and topological environments in oxides
… set of two lithium polyhedra and one empty polyhedron, the coordination polyhedra tend to be either 6-4-6 or 4-6-4 with the empty polyhedron in the center. Finally, we utilize the database to evaluate Pauling's first and second rules, which are guidelines for current understanding of …
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CRYSTAL CHEMISTRY AND PHYSICAL-CHEMICAL BEHAVIOR OF REE-BEARING PHOSPHATES AND ARSENATES: THE CASE STUDY OF MT. CERVANDONE
… of the TO4 tetrahedron, but even that of the REE-polyhedron, irrespective of the A-site population. An exception is provided by the relative abundance of Th and Ca at the A-site, which was found to expand the coordination polyhedron and unit-cell volumes irrespective of the T-site composition. The …
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Grid Domains for Analysing Software
… rep- resentation intersects a point of the grid-polyhedron. We provide an algorithm to compute the weakly tight product and show for what circumstances this algorithm achieves stronger results, so that the resulting grid-polyhedron is either a tight or a reduced product. Methods for test- ing if …
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Transformations preserving tame sets
… a triangulation and if P is a homeomorph of a polyhedron in X with respect to this triangulation, then P is tame in X if there is a homeomorphism h of X onto itself and another triangulation of X in which h(P) is a polyhedron. A function from one complex X into a complex is called tame and is …
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Vertex enumeration and counting for certain classes of polyhedra
… or all solutions that lie at corners of a convex polyhedron defined by a set of linear inequalities. Many algorithms have been developed for general polytopes. The most successful of these, from both an empirical and theoretical viewpoint, are based on pivoting. Dyer [24] gives an algorithm for …
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Spectral hulls: a degree of freedom reducing hp-strategy in space/time
… form relation for the Lebesgue constant on a polyhedron, derivation of a closed form relation for approximate Fekete points on a polyhedron and a new proof of Weierstrass approximation theorem in a polyhedral subset of d-dimensional space. One application of the proposed hull basis is to …
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On folding and unfolding with linkages and origami
… continuously flatten the surface of any convex polyhedron without distorting intrinsic surface distances or letting the surface pierce itself. This origami motion is quite general, and applies to convex polytopes of any dimension. To prove that no piercing occurs, we apply the same infinitesimal …
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