186 research outputs found
Computing tolerance parameters for fixturing and feeding
Fixtures and feeders are important components of automated assembly
systems: fixtures accurately hold parts and feeders move parts into alignment.
These components can fail when part shape varies. Parametric tolerance
classes specify how much variation is allowable. In this paper we consider
fixturing convex polygonal parts using right-angle brackets and feeding
polygonal parts on conveyor belts using sequences of vertical fences. For
both cases, we define new tolerance classes and give algorithms for computing
the parameter specifications such that the fixture or feeder will work for
all parts in the tolerance class. For fixturing we give an O(1) algorithm to
compute the dimensions of rectangular tolerance zones. For feeding we give
an O(n2) algorithm to compute the radius of the largest allowable tolerance
zone around each vertex. For each, we give an O(n) time algorithm for testing
if an n-sided part is in the tolerance class
Fast Locality-Sensitive Hashing Frameworks for Approximate Near Neighbor Search
The Indyk-Motwani Locality-Sensitive Hashing (LSH) framework (STOC 1998) is a
general technique for constructing a data structure to answer approximate near
neighbor queries by using a distribution over locality-sensitive
hash functions that partition space. For a collection of points, after
preprocessing, the query time is dominated by evaluations
of hash functions from and hash table lookups and
distance computations where is determined by the
locality-sensitivity properties of . It follows from a recent
result by Dahlgaard et al. (FOCS 2017) that the number of locality-sensitive
hash functions can be reduced to , leaving the query time to be
dominated by distance computations and
additional word-RAM operations. We state this result as a general framework and
provide a simpler analysis showing that the number of lookups and distance
computations closely match the Indyk-Motwani framework, making it a viable
replacement in practice. Using ideas from another locality-sensitive hashing
framework by Andoni and Indyk (SODA 2006) we are able to reduce the number of
additional word-RAM operations to .Comment: 15 pages, 3 figure
Bringing Order to Special Cases of Klee's Measure Problem
Klee's Measure Problem (KMP) asks for the volume of the union of n
axis-aligned boxes in d-space. Omitting logarithmic factors, the best algorithm
has runtime O*(n^{d/2}) [Overmars,Yap'91]. There are faster algorithms known
for several special cases: Cube-KMP (where all boxes are cubes), Unitcube-KMP
(where all boxes are cubes of equal side length), Hypervolume (where all boxes
share a vertex), and k-Grounded (where the projection onto the first k
dimensions is a Hypervolume instance).
In this paper we bring some order to these special cases by providing
reductions among them. In addition to the trivial inclusions, we establish
Hypervolume as the easiest of these special cases, and show that the runtimes
of Unitcube-KMP and Cube-KMP are polynomially related. More importantly, we
show that any algorithm for one of the special cases with runtime T(n,d)
implies an algorithm for the general case with runtime T(n,2d), yielding the
first non-trivial relation between KMP and its special cases. This allows to
transfer W[1]-hardness of KMP to all special cases, proving that no n^{o(d)}
algorithm exists for any of the special cases under reasonable complexity
theoretic assumptions. Furthermore, assuming that there is no improved
algorithm for the general case of KMP (no algorithm with runtime O(n^{d/2 -
eps})) this reduction shows that there is no algorithm with runtime
O(n^{floor(d/2)/2 - eps}) for any of the special cases. Under the same
assumption we show a tight lower bound for a recent algorithm for 2-Grounded
[Yildiz,Suri'12].Comment: 17 page
Computing the Fréchet Distance with a Retractable Leash
All known algorithms for the Fréchet distance between curves proceed in two steps: first, they construct an efficient oracle for the decision version; second, they use this oracle to find the optimum from a finite set of critical values. We present a novel approach that avoids the detour through the decision version. This gives the first quadratic time algorithm for the Fréchet distance between polygonal curves in (Formula presented.) under polyhedral distance functions (e.g., (Formula presented.) and (Formula presented.)). We also get a (Formula presented.)-approximation of the Fréchet distance under the Euclidean metric, in quadratic time for any fixed (Formula presented.). For the exact Euclidean case, our framework currently yields an algorithm with running time (Formula presented.). However, we conjecture that it may eventually lead to a faster exact algorithm
Testing for Network and Spatial Autocorrelation
Testing for dependence has been a well-established component of spatial
statistical analyses for decades. In particular, several popular test
statistics have desirable properties for testing for the presence of spatial
autocorrelation in continuous variables. In this paper we propose two
contributions to the literature on tests for autocorrelation. First, we propose
a new test for autocorrelation in categorical variables. While some methods
currently exist for assessing spatial autocorrelation in categorical variables,
the most popular method is unwieldy, somewhat ad hoc, and fails to provide
grounds for a single omnibus test. Second, we discuss the importance of testing
for autocorrelation in data sampled from the nodes of a network, motivated by
social network applications. We demonstrate that our proposed statistic for
categorical variables can both be used in the spatial and network setting
Parallel Write-Efficient Algorithms and Data Structures for Computational Geometry
In this paper, we design parallel write-efficient geometric algorithms that
perform asymptotically fewer writes than standard algorithms for the same
problem. This is motivated by emerging non-volatile memory technologies with
read performance being close to that of random access memory but writes being
significantly more expensive in terms of energy and latency. We design
algorithms for planar Delaunay triangulation, -d trees, and static and
dynamic augmented trees. Our algorithms are designed in the recently introduced
Asymmetric Nested-Parallel Model, which captures the parallel setting in which
there is a small symmetric memory where reads and writes are unit cost as well
as a large asymmetric memory where writes are times more expensive
than reads. In designing these algorithms, we introduce several techniques for
obtaining write-efficiency, including DAG tracing, prefix doubling,
reconstruction-based rebalancing and -labeling, which we believe will
be useful for designing other parallel write-efficient algorithms
Developing serious games for cultural heritage: a state-of-the-art review
Although the widespread use of gaming for leisure purposes has been well documented, the use of games to support cultural heritage purposes, such as historical teaching and learning, or for enhancing museum visits, has been less well considered. The state-of-the-art in serious game technology is identical to that of the state-of-the-art in entertainment games technology. As a result, the field of serious heritage games concerns itself with recent advances in computer games, real-time computer graphics, virtual and augmented reality and artificial intelligence. On the other hand, the main strengths of serious gaming applications may be generalised as being in the areas of communication, visual expression of information, collaboration mechanisms, interactivity and entertainment. In this report, we will focus on the state-of-the-art with respect to the theories, methods and technologies used in serious heritage games. We provide an overview of existing literature of relevance to the domain, discuss the strengths and weaknesses of the described methods and point out unsolved problems and challenges. In addition, several case studies illustrating the application of methods and technologies used in cultural heritage are presented
SeqAn An efficient, generic C++ library for sequence analysis
<p>Abstract</p> <p>Background</p> <p>The use of novel algorithmic techniques is pivotal to many important problems in life science. For example the sequencing of the human genome <abbrgrp><abbr bid="B1">1</abbr></abbrgrp> would not have been possible without advanced assembly algorithms. However, owing to the high speed of technological progress and the urgent need for bioinformatics tools, there is a widening gap between state-of-the-art algorithmic techniques and the actual algorithmic components of tools that are in widespread use.</p> <p>Results</p> <p>To remedy this trend we propose the use of SeqAn, a library of efficient data types and algorithms for sequence analysis in computational biology. SeqAn comprises implementations of existing, practical state-of-the-art algorithmic components to provide a sound basis for algorithm testing and development. In this paper we describe the design and content of SeqAn and demonstrate its use by giving two examples. In the first example we show an application of SeqAn as an experimental platform by comparing different exact string matching algorithms. The second example is a simple version of the well-known MUMmer tool rewritten in SeqAn. Results indicate that our implementation is very efficient and versatile to use.</p> <p>Conclusion</p> <p>We anticipate that SeqAn greatly simplifies the rapid development of new bioinformatics tools by providing a collection of readily usable, well-designed algorithmic components which are fundamental for the field of sequence analysis. This leverages not only the implementation of new algorithms, but also enables a sound analysis and comparison of existing algorithms.</p
A randomized attitude slew planning algorithm for autonomous spacecraft
The ability to autonomously generate and execute large angle attitude maneuvers, while operating under a number of celestial and dynamical constraints, is a key factor in the development of several future space platforms. In this paper we propose a ran-domized attitude slew planning algorithm for autonomous spacecraft, which is able to address a variety of pointing constraints, including bright object avoidance and ground link maintenance, as well as constraints on the control inputs and spacecraft states, and integral constraints such as those deriving from thermal control requirements. Moreover, through the scheduling of feedback control policies, the algorithm provides a consistent decoupling between low-level control and attitude motion planning, and is robust with respect to uncertainties in the spacecraft dynamics and environmental disturbances. Sim-ulation examples are presented and discussed
Every Large Point Set contains Many Collinear Points or an Empty Pentagon
We prove the following generalised empty pentagon theorem: for every integer
, every sufficiently large set of points in the plane contains
collinear points or an empty pentagon. As an application, we settle the
next open case of the "big line or big clique" conjecture of K\'ara, P\'or, and
Wood [\emph{Discrete Comput. Geom.} 34(3):497--506, 2005]
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