5,887 research outputs found
Analysis of approximate nearest neighbor searching with clustered point sets
We present an empirical analysis of data structures for approximate nearest
neighbor searching. We compare the well-known optimized kd-tree splitting
method against two alternative splitting methods. The first, called the
sliding-midpoint method, which attempts to balance the goals of producing
subdivision cells of bounded aspect ratio, while not producing any empty cells.
The second, called the minimum-ambiguity method is a query-based approach. In
addition to the data points, it is also given a training set of query points
for preprocessing. It employs a simple greedy algorithm to select the splitting
plane that minimizes the average amount of ambiguity in the choice of the
nearest neighbor for the training points. We provide an empirical analysis
comparing these two methods against the optimized kd-tree construction for a
number of synthetically generated data and query sets. We demonstrate that for
clustered data and query sets, these algorithms can provide significant
improvements over the standard kd-tree construction for approximate nearest
neighbor searching.Comment: 20 pages, 8 figures. Presented at ALENEX '99, Baltimore, MD, Jan
15-16, 199
Delaunay triangulation and computational fluid dynamics meshes
In aerospace computational fluid dynamics (CFD) calculations, the Delaunay triangulation of suitable quadrilateral meshes can lead to unsuitable triangulated meshes. Here, we present case studies which illustrate the limitations of using structured grid generation methods which produce points in a curvilinear coordinate system for subsequent triangulations for CFD applications. We discuss conditions under which meshes of quadrilateral elements may not produce a Delaunay triangulation suitable for CFD calculations, particularly with regard to high aspect ratio, skewed quadrilateral elements
On the Combinatorial Complexity of Approximating Polytopes
Approximating convex bodies succinctly by convex polytopes is a fundamental
problem in discrete geometry. A convex body of diameter
is given in Euclidean -dimensional space, where is a constant. Given an
error parameter , the objective is to determine a polytope of
minimum combinatorial complexity whose Hausdorff distance from is at most
. By combinatorial complexity we mean the
total number of faces of all dimensions of the polytope. A well-known result by
Dudley implies that facets suffice, and a dual
result by Bronshteyn and Ivanov similarly bounds the number of vertices, but
neither result bounds the total combinatorial complexity. We show that there
exists an approximating polytope whose total combinatorial complexity is
, where conceals a
polylogarithmic factor in . This is a significant improvement
upon the best known bound, which is roughly .
Our result is based on a novel combination of both old and new ideas. First,
we employ Macbeath regions, a classical structure from the theory of convexity.
The construction of our approximating polytope employs a new stratified
placement of these regions. Second, in order to analyze the combinatorial
complexity of the approximating polytope, we present a tight analysis of a
width-based variant of B\'{a}r\'{a}ny and Larman's economical cap covering.
Finally, we use a deterministic adaptation of the witness-collector technique
(developed recently by Devillers et al.) in the context of our stratified
construction.Comment: In Proceedings of the 32nd International Symposium Computational
Geometry (SoCG 2016) and accepted to SoCG 2016 special issue of Discrete and
Computational Geometr
Space Exploration via Proximity Search
We investigate what computational tasks can be performed on a point set in
, if we are only given black-box access to it via nearest-neighbor
search. This is a reasonable assumption if the underlying point set is either
provided implicitly, or it is stored in a data structure that can answer such
queries. In particular, we show the following: (A) One can compute an
approximate bi-criteria -center clustering of the point set, and more
generally compute a greedy permutation of the point set. (B) One can decide if
a query point is (approximately) inside the convex-hull of the point set.
We also investigate the problem of clustering the given point set, such that
meaningful proximity queries can be carried out on the centers of the clusters,
instead of the whole point set
Coparenting and school success: perspectives of fathers.
Historically, measures of coparenting have been reported by mothers. As a result, fathers’ perspectives and experiences have largely been excluded from this body of research. In response, this study relies on fathers own report of coparenting support. This study used a sample of 1255 biological fathers from the Fragile Families and Child Wellbeing Study (FFCWS) to explore fathers’ reports of their coparenting support and how this is associated with relationship status with mother, time spent with child, and several school success variables including: internalizing and externalizing school behaviors and math and reading assessment scores at child age 9. Hypotheses included that higher coparenting reports would be positively associated with married and romantic cohabitating fathers as well as fathers who spent more time with their child. Additionally, it was hypothesized that higher father coparenting reports would predict lower internalizing and externalizing behaviors and increased reading and math scores. While support was found for relationship status and time spent with child coparenting hypotheses, there was little support for the school variables to be significantly predicted by coparenting reports. Two control variables (race/ethnicity and poverty to income level) did yield consistent results for predicting school outcome variables. Future research should continue to focus on the equity of how coparenting is measured and reported and how the coparenting relationship is significant in healthy child development
Evaluation of the Heritage Lottery Fund Landscape Partnership Programme: report to the Heritage Lottery Fund
Correspondence between HBT radii and the emission zone in non-central heavy ion collisions
In non-central collisions between ultra-relativistic heavy ions, the
freeze-out distribution is anisotropic, and its major longitudinal axis may be
tilted away from the beam direction. The shape and orientation of this
distribution are particularly interesting, as they provide a snapshot of the
evolving source and reflect the space-time aspect of anisotropic flow.
Experimentally, this information is extracted by measuring pion HBT radii as a
function of angle with respect to the reaction plane. Existing formulae
relating the oscillations of the radii and the freezeout anisotropy are in
principle only valid for Gaussian sources with no collective flow. With a
realistic transport model of the collision, which generates flow and
non-Gaussian sources, we find that these formulae approximately reflect the
anisotropy of the freezeout distribution.Comment: 9 pages, 8 figure
Performance, emissions, and physical characteristics of a rotating combustion aircraft engine
The RC2-75, a liquid cooled two chamber rotary combustion engine (Wankel type), designed for aircraft use, was tested and representative baseline (212 KW, 285 BHP) performance and emissions characteristics established. The testing included running fuel/air mixture control curves and varied ignition timing to permit selection of desirable and practical settings for running wide open throttle curves, propeller load curves, variable manifold pressure curves covering cruise conditions, and EPA cycle operating points. Performance and emissions data were recorded for all of the points run. In addition to the test data, information required to characterize the engine and evaluate its performance in aircraft use is provided over a range from one half to twice its present power. The exhaust emissions results are compared to the 1980 EPA requirements. Standard day take-off brake specific fuel consumption is 356 g/KW-HR (.585 lb/BHP-HR) for the configuration tested
Online Algorithms for Warehouse Management
As the prevalence of E-commerce continues to grow, the efficient operation of warehouses and fulfillment centers is becoming increasingly important. To this end, many such warehouses are adding automation in order to help streamline operations, drive down costs, and increase overall efficiency. The introduction of automation comes with the opportunity for new theoretical models and computational problems with which to better understand and optimize such systems.
These systems often maintain a warehouse of standardized portable storage units, which are stored and retrieved by robotic workers. In general, there are two principal issues in optimizing such a system: where in the warehouse each storage unit should be located and how best to retrieve them. These two concerns naturally go hand-in-hand, but are further complicated by the unknown request frequencies of stored products. Analogous to virtual-memory systems, the more popular and oft-requested an item is, the more efficient its retrieval should be. In this paper, we propose a theoretical model for organizing portable storage units in a warehouse subject to an online sequence of access requests. We consider two formulations, depending on whether there is a single access point or multiple access points. We present algorithms that are O(1)-competitive with respect to an optimal algorithm. In the case of a single access point, our solution is also asymptotically optimal with respect to density
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