Related papers: The Case for Distance-Bounded Spatial Approximatio…
Traditional problems in computational geometry involve aspects that are both discrete and continuous. One such example is nearest-neighbor searching, where the input is discrete, but the result depends on distances, which vary continuously.…
Many new database application domains such as experimental sciences and medicine are characterized by large sequences as their main form of data. Using approximate representation can significantly reduce the required storage and search…
Over the past a few years, research and development has made significant progresses on big data analytics. A fundamental issue for big data analytics is the efficiency. If the optimal solution is unable to attain or not required or has a…
Spatial data is playing an emerging role in new technologies such as web and mobile mapping and Geographic Information Systems (GIS). Important decisions in political, social and many other aspects of modern human life are being made using…
The amount of the available geospatial data grows at an ever faster pace. This leads to the constantly increasing demand for processing power and storage in order to provide data analysis in a timely manner. At the same time, a lot of…
The rapid growth of demanding applications in domains applying multimedia processing and machine learning has marked a new era for edge and cloud computing. These applications involve massive data and compute-intensive tasks, and thus,…
Functions of one or more variables are usually approximated with a basis: a complete, linearly-independent system of functions that spans a suitable function space. The topic of this paper is the numerical approximation of functions using…
Conformance checking techniques let us find out to what degree a process model and real execution data correspond to each other. In recent years, alignments have proven extremely useful in calculating conformance statistics. Most techniques…
In algorithms for finite metric spaces, it is common to assume that the distance between two points can be computed in constant time, and complexity bounds are expressed only in terms of the number of points of the metric space. We…
Comparison to traditionally accurate computing, approximate computing focuses on the rapidity of the satisfactory solution, but not the unnecessary accuracy of the solution. Approximate bisimularity is the approximate one corresponding to…
Surveillance and surveying are two important applications of empirical research. A major part of terrain modelling is supported by photographic surveys which are used for capturing expansive natural surfaces using a wide range of sensors --…
In [Heimann, Lehrenfeld, Preu{\ss}, SIAM J. Sci. Comp. 45(2), 2023, B139 - B165] new geometrically unfitted space-time Finite Element methods for partial differential equations posed on moving domains of higher-order accuracy in space and…
Rectangles are used to approximate objects, or sets of objects, in a plethora of applications, systems and index structures. Many tasks, such as nearest neighbor search and similarity ranking, require to decide if objects in one rectangle A…
Spatial join processing techniques that identify intersections between complex geometries (e.g., polygons) commonly follow a two-step filter-and-refine pipeline. The filter step evaluates the query predicate on the minimum bounding…
Numerical approximate computation can solve large and complex problems fast. It has the advantage of high efficiency. However it only gives approximate results, whereas we need exact results in many fields. There is a gap between…
Approximation of scattered data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for big scattered datasets in $n-$dimensional space. It is a non-separable approximation, as it is…
Many problems in computer vision can be formulated as geometric estimation problems, i.e. given a collection of measurements (e.g. point correspondences) we wish to fit a model (e.g. an essential matrix) that agrees with our observations.…
The use of approximation is fundamental in computational science. Almost all computational methods adopt approximations in some form in order to obtain a favourable cost/accuracy trade-off and there are usually many approximations that…
Approximate K Nearest Neighbor (AKNN) search in high-dimensional spaces is a critical yet challenging problem. In AKNN search, distance computation is the core task that dominates the runtime. Existing approaches typically use approximate…
When planning motions in a configuration space that has underlying symmetries (e.g. when manipulating one or multiple symmetric objects), the ideal planning algorithm should take advantage of those symmetries to produce shorter…