1,357 research outputs found
Constructing Binary Space Partitions for Orthogonal Rectangles in Practice
The original publication is available at www.springerlink.comIn this paper, we develop a simple technique for constructing
a I3inary Space Partition (nSP) for a set of orthogonal rectangles in IR3.
OUf algorithm has the novel feature that it tunes its performance to the
geometric properties of the rectangles, e.g., their aspect ratios.
"Fe have implemented our algorithm and tested its performance on real
data scti). V\.Tc have also systematically compared the performance of our
algorithm with that of other techniques presented in the literature. Our
studies show that our algorithm constructs nsps of near-linear size and
small height in practice, has fast running times, and answers queries
efficiently. It is a method of choice for constructing BSPs for orthogonal
rectangles
Binary Space Partitions for Fat Rectangles
This is the published version. Copyright © 2000 Society for Industrial and Applied Mathematic
A Framework for Index Bulk Loading and Dynamization
In this paper we investigate automated methods for externalizing
internal memory data structures. We consider a class of balanced trees that we
call weight-balanced partitioning trees (or wp-trees) for indexing a set of points
in Rd. Well-known examples of wp-trees include fed-trees, BBD-trees, pseudo
quad trees, and BAR trees. These trees are defined with fixed degree and are
thus suited for internal memory implementations. Given an efficient wp-tree
construction algorithm, we present a general framework for automatically obtaining
a new dynamic external data structure. Using this framework together
with a new general construction (bulk loading) technique of independent interest,
we obtain data structures with guaranteed good update performance in
terms of I /O transfers. Our approach gives considerably improved construction
and update I/O bounds of e.g. fed-trees and BBD-trees
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
A practical and robust method to compute the boundary of three-dimensional axis-aligned boxes
The union of axis-aligned boxes results in a constrained structure that is advantageous for solving certain geometrical problems. A widely used scheme for solid modelling systems is the boundary representation (Brep). We present a method to obtain the B-rep of a union of axis-aligned boxes. Our method computes all boundary vertices, and additional information for each vertex that allows us to apply already existing methods to extract the B-rep. It is based on dividing the three-dimensional problem into two-dimensional boundary computations and combining their results. The method can deal with all geometrical degeneracies that may arise. Experimental results prove that our approach outperforms existing general methods, both in efficiency and robustness.)Peer ReviewedPostprint (author’s final draft
Multi-Sided Boundary Labeling
In the Boundary Labeling problem, we are given a set of points, referred
to as sites, inside an axis-parallel rectangle , and a set of pairwise
disjoint rectangular labels that are attached to from the outside. The task
is to connect the sites to the labels by non-intersecting rectilinear paths,
so-called leaders, with at most one bend.
In this paper, we study the Multi-Sided Boundary Labeling problem, with
labels lying on at least two sides of the enclosing rectangle. We present a
polynomial-time algorithm that computes a crossing-free leader layout if one
exists. So far, such an algorithm has only been known for the cases in which
labels lie on one side or on two opposite sides of (here a crossing-free
solution always exists). The case where labels may lie on adjacent sides is
more difficult. We present efficient algorithms for testing the existence of a
crossing-free leader layout that labels all sites and also for maximizing the
number of labeled sites in a crossing-free leader layout. For two-sided
boundary labeling with adjacent sides, we further show how to minimize the
total leader length in a crossing-free layout
RRR: Rank-Regret Representative
Selecting the best items in a dataset is a common task in data exploration.
However, the concept of "best" lies in the eyes of the beholder: different
users may consider different attributes more important, and hence arrive at
different rankings. Nevertheless, one can remove "dominated" items and create a
"representative" subset of the data set, comprising the "best items" in it. A
Pareto-optimal representative is guaranteed to contain the best item of each
possible ranking, but it can be almost as big as the full data. Representative
can be found if we relax the requirement to include the best item for every
possible user, and instead just limit the users' "regret". Existing work
defines regret as the loss in score by limiting consideration to the
representative instead of the full data set, for any chosen ranking function.
However, the score is often not a meaningful number and users may not
understand its absolute value. Sometimes small ranges in score can include
large fractions of the data set. In contrast, users do understand the notion of
rank ordering. Therefore, alternatively, we consider the position of the items
in the ranked list for defining the regret and propose the {\em rank-regret
representative} as the minimal subset of the data containing at least one of
the top- of any possible ranking function. This problem is NP-complete. We
use the geometric interpretation of items to bound their ranks on ranges of
functions and to utilize combinatorial geometry notions for developing
effective and efficient approximation algorithms for the problem. Experiments
on real datasets demonstrate that we can efficiently find small subsets with
small rank-regrets
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