21,491 research outputs found
Multidimensional Range Queries on Modern Hardware
Range queries over multidimensional data are an important part of database
workloads in many applications. Their execution may be accelerated by using
multidimensional index structures (MDIS), such as kd-trees or R-trees. As for
most index structures, the usefulness of this approach depends on the
selectivity of the queries, and common wisdom told that a simple scan beats
MDIS for queries accessing more than 15%-20% of a dataset. However, this wisdom
is largely based on evaluations that are almost two decades old, performed on
data being held on disks, applying IO-optimized data structures, and using
single-core systems. The question is whether this rule of thumb still holds
when multidimensional range queries (MDRQ) are performed on modern
architectures with large main memories holding all data, multi-core CPUs and
data-parallel instruction sets. In this paper, we study the question whether
and how much modern hardware influences the performance ratio between index
structures and scans for MDRQ. To this end, we conservatively adapted three
popular MDIS, namely the R*-tree, the kd-tree, and the VA-file, to exploit
features of modern servers and compared their performance to different flavors
of parallel scans using multiple (synthetic and real-world) analytical
workloads over multiple (synthetic and real-world) datasets of varying size,
dimensionality, and skew. We find that all approaches benefit considerably from
using main memory and parallelization, yet to varying degrees. Our evaluation
indicates that, on current machines, scanning should be favored over parallel
versions of classical MDIS even for very selective queries
Ptolemaic Indexing
This paper discusses a new family of bounds for use in similarity search,
related to those used in metric indexing, but based on Ptolemy's inequality,
rather than the metric axioms. Ptolemy's inequality holds for the well-known
Euclidean distance, but is also shown here to hold for quadratic form metrics
in general, with Mahalanobis distance as an important special case. The
inequality is examined empirically on both synthetic and real-world data sets
and is also found to hold approximately, with a very low degree of error, for
important distances such as the angular pseudometric and several Lp norms.
Indexing experiments demonstrate a highly increased filtering power compared to
existing, triangular methods. It is also shown that combining the Ptolemaic and
triangular filtering can lead to better results than using either approach on
its own
Performance comparison of point and spatial access methods
In the past few years a large number of multidimensional point access methods, also called
multiattribute index structures, has been suggested, all of them claiming good performance. Since no
performance comparison of these structures under arbitrary (strongly correlated nonuniform, short
"ugly") data distributions and under various types of queries has been performed, database
researchers and designers were hesitant to use any of these new point access methods. As shown in
a recent paper, such point access methods are not only important in traditional database applications.
In new applications such as CAD/CIM and geographic or environmental information systems, access
methods for spatial objects are needed. As recently shown such access methods are based on point
access methods in terms of functionality and performance. Our performance comparison naturally
consists of two parts. In part I we w i l l compare multidimensional point access methods, whereas in
part I I spatial access methods for rectangles will be compared. In part I we present a survey and
classification of existing point access methods. Then we carefully select the following four methods
for implementation and performance comparison under seven different data files (distributions) and
various types of queries: the 2-level grid file, the BANG file, the hB-tree and a new scheme, called
the BUDDY hash tree. We were surprised to see one method to be the clear winner which was the
BUDDY hash tree. It exhibits an at least 20 % better average performance than its competitors and is
robust under ugly data and queries. In part I I we compare spatial access methods for rectangles.
After presenting a survey and classification of existing spatial access methods we carefully selected
the following four methods for implementation and performance comparison under six different data
files (distributions) and various types of queries: the R-tree, the BANG file, PLOP hashing and the
BUDDY hash tree. The result presented two winners: the BANG file and the BUDDY hash tree.
This comparison is a first step towards a standardized testbed or benchmark. We offer our data and
query files to each designer of a new point or spatial access method such that he can run his
implementation in our testbed
Using Visualization to Support Data Mining of Large Existing Databases
In this paper. we present ideas how visualization technology can be used to improve the difficult process of querying very large databases. With our VisDB system, we try to provide visual support not only for the query specification process. but also for evaluating query results and. thereafter, refining the query accordingly. The main idea of our system is to represent as many data items as possible by the pixels of the display device. By arranging and coloring the pixels according to the relevance for the query, the user gets a visual impression of the resulting data set and of its relevance for the query. Using an interactive query interface, the user may change the query dynamically and receives immediate feedback by the visual representation of the resulting data set. By using multiple windows for different parts of the query, the user gets visual feedback for each part of the query and, therefore, may easier understand the overall result. To support complex queries, we introduce the notion of approximate joins which allow the user to find data items that only approximately fulfill join conditions. We also present ideas how our technique may be extended to support the interoperation of heterogeneous databases. Finally, we discuss the performance problems that are caused by interfacing to existing database systems and present ideas to solve these problems by using data structures supporting a multidimensional search of the database
Massive Nonplanar Two-Loop Maximal Unitarity
We explore maximal unitarity for nonplanar two-loop integrals with up to four
massive external legs. In this framework, the amplitude is reduced to a basis
of master integrals whose coefficients are extracted from maximal cuts. The
hepta-cut of the nonplanar double box defines a nodal algebraic curve
associated with a multiply pinched genus-3 Riemann surface. All possible
configurations of external masses are covered by two distinct topological
pictures in which the curve decomposes into either six or eight Riemann
spheres. The procedure relies on consistency equations based on vanishing of
integrals of total derivatives and Levi-Civita contractions. Our analysis
indicates that these constraints are governed by the global structure of the
maximal cut. Lastly, we present an algorithm for computing generalized cuts of
massive integrals with higher powers of propagators based on the Bezoutian
matrix method.Comment: 54 pages, 9 figures, v2: journal versio
A L\'evy area by Fourier normal ordering for multidimensional fractional Brownian motion with small Hurst index
The main tool for stochastic calculus with respect to a multidimensional
process with small H\"older regularity index is rough path theory. Once
has been lifted to a rough path, a stochastic calculus -- as well as solutions
to stochastic differential equations driven by -- follow by standard
arguments. Although such a lift has been proved to exist by abstract arguments
\cite{LyoVic07}, a first general, explicit construction has been proposed in
\cite{Unt09,Unt09bis} under the name of Fourier normal ordering. The purpose of
this short note is to convey the main ideas of the Fourier normal ordering
method in the particular case of the iterated integrals of lowest order of
fractional Brownian motion with arbitrary Hurst index.Comment: 20 page
- …