Assuming GCH $\mathsf {GCH}$ , we show that generalized eventually narrow sequences on a strongly inaccessible cardinal κ are preserved under one step iteration of the Hechler forcing for adding dominating κ-real. Moreover, if is unfoldable, 2 = + $2^\kappa =\kappa ^+$ and λ regular such < $\kappa ^+ \lambda$ then there set generic extension in which s ( ) b c $\mathfrak {s}(\kappa \kappa \math...

We introduce a new type of bounding-volume hierarchy, the c-oriented rotated-box tree, or c-rb-tree for short. A c-rb-tree uses boxes as bounding volumes, whose orientations come from a fixed set of predefined box orientations. We theoretically and experimentally compare our new c-rb-tree to two existing bounding-volumes hierarchies, namely c-dop-trees and box-trees.

The Real-time collision detection (CD) is an important problem in virtual environments. This paper proposes a novel algorithm called SBBK which combines three different kinds of bounding volumes (BVs) together when constructing the hybrid bounding box tree for the object to make CD more accurate and faster. For illustration, CD experiments are carried out to show its advantages. The experiment ...

This paper presents a scheduling problem with unrelated parallel machines and sequencedependent setup times that minimizes the total weighted tardiness. A new branch-and-bound (B and B) algorithm is designed incorporating the lower and upper bounding schemes and several dominance properties. The lower and upper bounds are derived through an assignment problem and the composite dispatching rule ...

We present an algorithm to construct a bounding polyhedron for an affine Iterated Function System (IFS). Our algorithm expresses the IFS-bounding problem as a set of linear constraints on a linear objective function, which can then be solved via standard techniques for linear convex optimization. As such, our algorithm is guaranteed to find the optimum recursively instantiable bounding volume, ...

Methods for computing tight bounding volumes for general parametric surfaces, for testing if two bounding volumes intersect and for computing inclusions for the intersection of two bounding volumes are discussed. These methods together with interval arithmetic are the basis for a robust algorithm for computing inclusions for all parts of the intersection curve of two general parametric surfaces.

We propose a variational approach to computing an optimal segmentation of a 3D shape for computing a union of tight bounding volumes. Based on an affine invariant measure of e-tightness, the resemblance to ellipsoid, a novel functional is formulated that governs an optimization process to obtain a partition with multiple components. Refinement of segmentation is driven by application-specific e...

Beam-ACO algorithms are hybrid methods that combine the metaheuristic ant colony optimization with beam search. They heavily rely on accurate and computationally inexpensive bounding information for choosing between different partial solutions during the solution construction process. In this work we present the use of stochastic sampling as a useful alternative to bounding information in cases...

We provide a simple suffi cient condition for the existence of a recursive upper bound on the sequential equilibrium payoff set at a fixed discount factor in two-player repeated games with imperfect private monitoring. The bounding set is the sequential equilibrium payoff set with perfect monitoring and a mediator. We show that this bounding set admits a simple recursive characterization, which...