A Potential-Field-Based Multilevel Algorithm for Drawing Large Graphs

The aim of automatic graph drawing is to compute a well-readable layout of a given graph G=(V,E). One very popular class of algorithms for drawing general graphs are force-directed methods. These methods generate drawings of G in the plane so that each edge is represented by a straight line connecting its two adjacent nodes. The computation of the drawings is based on associating G with a physical model. Then, the algorithms iteratively try to find a placement of the nodes so that the total energy of the physical system is minimal. Several force-directed methods can visualize large graphs containing many thousands of vertices in reasonable time. However, only some of these methods guarantee a sub-quadratic running time in special cases or under certain assumptions, but not in general. The others are not sub-quadratic at all. We develop a new force-directed algorithm that is based on a combination of an efficient multilevel strategy and a method for approximating the repulsive forces in the system by rapidly evaluating potential fields. The worst-case running time of the new method is O(|V| log|V|+|E|) with linear memory requirements. In practice, the algorithm generates nice drawings of graphs containing up to 100000 nodes in less than five minutes. Furthermore, it clearly visualizes even the structures of those graphs that turned out to be challenging for other tested methods

6 Access Methods and Query Processing Techniques

The performance of a database management system (DBMS) is fundamentally dependent on the access methods and query processing techniques available to the system. Traditionally, relational DBMSs have relied on well-known access methods, such as the ubiquitous B +-tree, hashing with chaining, and, in som

Query processing of geometric objects with free form boundarie sin spatial databases

The increasing demand for the use of database systems as an integrating factor in CAD/CAM applications has necessitated the development of database systems with appropriate modelling and retrieval capabilities. One essential problem is the treatment of geometric data which has led to the development of spatial databases. Unfortunately, most proposals only deal with simple geometric objects like multidimensional points and rectangles. On the other hand, there has been a rapid development in the field of representing geometric objects with free form curves or surfaces, initiated by engineering applications such as mechanical engineering, aviation or astronautics. Therefore, we propose a concept for the realization of spatial retrieval operations on geometric objects with free form boundaries, such as B-spline or Bezier curves, which can easily be integrated in a database management system. The key concept is the encapsulation of geometric operations in a so-called query processor. First, this enables the definition of an interface allowing the integration into the data model and the definition of the query language of a database system for complex objects. Second, the approach allows the use of an arbitrary representation of the geometric objects. After a short description of the query processor, we propose some representations for free form objects determined by B-spline or Bezier curves. The goal of efficient query processing in a database environment is achieved using a combination of decomposition techniques and spatial access methods. Finally, we present some experimental results indicating that the performance of decomposition techniques is clearly superior to traditional query processing strategies for geometric objects with free form boundaries

Adaptive Mesh Refinement Strategy for the Semi-Analytical Solution of Frictionless Elastic Contact Problems

Semi-analytical methods are commonly used to solve contact problems. These methods require the discretization of the domain into a mesh of pressure elements. In general, it can be said that their accuracy increases as the pressure element mesh is refined. However, the refinement of the pressure element mesh also implies an increase in their computational cost. So, in the great majority of the cases, a commitment between accuracy and computational cost must be achieved. In this work, a new approach is presented, whose main purpose is to improve the efficiency of the semi-analytical methods that are used to solve contact problems. To do so, an adaptive refinement of the pressure element mesh is implemented. This strategy allows for a reduction of the computational cost of the method, while its accuracy remains unaffected

Adaptive global optimization algorithms

Global optimization is concerned with finding the minimum value of a function where many local minima may exist. The development of a global optimization algorithm may involve using information about the target function (e.g., differentiability) and functions based on statistical models to better the worst case time complexity and expected error of similar deterministic algorithms. Recent algorithms are investigated, new ones proposed and their performance is analyzed. Minimum, maximum and average case error bounds for the algorithms presented are derived. Software architecture implemented with MATLAB and Java is presented and experimental results for the algorithms are displayed. The graphical capabilities and function-rich MATLAB environment are combined with the object oriented features of Java, hosted on the computer system described in this paper, to provide a fast, powerful test environment to provide experimental results. In order to do this, matlabcontrol, a third party set of procedures that allows a Java program to call MATLAB functions to access a function such as voronoi() or to provide graphical results, is used. Additionally, the Java implementation can be called from, and return values to, the MATLAB environment. The data can then be used as input to MATLAB\u27s graphing or other functions. The software test environment provides algorithm performance information such as whether more iterations or replications of a proposed algorithm would be expected to provide a better result for an algorithm. It is anticipated that the functionality provided by the framework would be used for initial development and analysis and subsequently removed and replaced with optimized (in the computer efficiency sense) functions for deployment

High Performance Spatial Indexing for Parallel I/O and Centralized Architectures

Recently, spatial databases have attracted increasing interest in the database field. Because of the volume of the data with which they deal with, the performance of spatial database systems' is important. The R-tree is an efficient spatial access method. It is a generalization of the B-tree in multidimensional space. This thesis investigates how to improve the performance of R-trees. We consider both parallel I/O and centralized architectures. For a parallel I/O environment we propose an R-tree design for a server with one CPU and multiple disks. On this architecture, the nodes of the R-tree are distributed between the different disks with cross-disk pointers ( 'Multiplezed R-tree a). When a new node is created we have to decide on which disk it will be stored. We propose and examine several criteria for choosing a disk for a new node. The most successful one, termed 'Prozimity Indew' or PI, estimates the similarity of the new node to other R-tree nodes already on a disk and chooses the disk with the least degree of similarity. For a centralized environment, we propose a new packing technique for R-trees for static databases. We use space-filling curves, and specifically the Hilbert curve, to achieve better ordering of rectangles and eventually to achieve better packing. For dynamic databases we introduce the filbert R-tree, in which every node has a well defined set of sibling nodes; we can thus use the concept of local rotation [47]. By adjusting the split policy, the Filbert R-tree can achieve a degree of space utilization as high as is desired. (Also cross-referenced as UMIACS-TR-94-131

A Potential-Field-Based Multilevel Algorithm for Drawing Large Graphs

The aim of automatic graph drawing is to compute a well-readable layout of a given graph G=(V,E). One very popular class of algorithms for drawing general graphs are force-directed methods. These methods generate drawings of G in the plane so that each edge is represented by a straight line connecting its two adjacent nodes. The computation of the drawings is based on associating G with a physical model. Then, the algorithms iteratively try to find a placement of the nodes so that the total energy of the physical system is minimal. Several force-directed methods can visualize large graphs containing many thousands of vertices in reasonable time. However, only some of these methods guarantee a sub-quadratic running time in special cases or under certain assumptions, but not in general. The others are not sub-quadratic at all. We develop a new force-directed algorithm that is based on a combination of an efficient multilevel strategy and a method for approximating the repulsive forces in the system by rapidly evaluating potential fields. The worst-case running time of the new method is O(|V| log|V|+|E|) with linear memory requirements. In practice, the algorithm generates nice drawings of graphs containing up to 100000 nodes in less than five minutes. Furthermore, it clearly visualizes even the structures of those graphs that turned out to be challenging for other tested methods

Geographic Information Systems: The Developer\u27s Perspective

Geographic information systems, which manage data describing the surface of the earth, are becoming increasingly popular. This research details the current state of the art of geographic data processing in terms of the needs of the geographic information system developer. The research focuses chiefly on the geographic data model--the basic building block of the geographic information system. The two most popular models, tessellation and vector, are studied in detail, as well as a number of hybrid data models. In addition, geographic database management is discussed in terms of geographic data access and query processing. Finally, a pragmatic discussion of geographic information system design is presented covering such topics as distributed database considerations and artificial intelligence considerations

Enhancing In-Memory Spatial Indexing with Learned Search

Spatial data is ubiquitous. Massive amounts of data are generated every day from a plethora of sources such as billions of GPS-enableddevices (e.g., cell phones, cars, and sensors), consumer-based applications (e.g., Uber and Strava), and social media platforms (e.g.,location-tagged posts on Facebook, Twitter, and Instagram). This exponential growth in spatial data has led the research communityto build systems and applications for efficient spatial data processing.In this study, we apply a recently developed machine-learned search technique for single-dimensional sorted data to spatial indexing.Specifically, we partition spatial data using six traditional spatial partitioning techniques and employ machine-learned search withineach partition to support point, range, distance, and spatial join queries. Adhering to the latest research trends, we tune the partitioningtechniques to be instance-optimized. By tuning each partitioning technique for optimal performance, we demonstrate that: (i) grid-basedindex structures outperform tree-based index structures (from 1.23× to 2.47×), (ii) learning-enhanced variants of commonly used spatialindex structures outperform their original counterparts (from 1.44× to 53.34× faster), (iii) machine-learned search within a partitionis faster than binary search by 11.79% - 39.51% when filtering on one dimension, (iv) the benefit of machine-learned search diminishesin the presence of other compute-intensive operations (e.g. scan costs in higher selectivity queries, Haversine distance computation, andpoint-in-polygon tests), and (v) index lookup is the bottleneck for tree-based structures, which could potentially be reduced by linearizingthe indexed partitions.Additional Key Words and Phrases: spatial data, indexing, machine-learning, spatial queries, geospatia