Optimal quadtree construction algorithms
Computer Vision, Graphics, and Image Processing
A formula for computing the number of quadtree node fragments created by a shift
Pattern Recognition Letters
Redundancy in spatial databases
SIGMOD '89 Proceedings of the 1989 ACM SIGMOD international conference on Management of data
The fieldtree: a data structure for geographic information systems
SSD '90 Proceedings of the first symposium on Design and implementation of large spatial databases
Hashing by proximity to process duplicates in spatial databases
CIKM '94 Proceedings of the third international conference on Information and knowledge management
Approximate nearest neighbor queries revisited
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
An effective way to represent quadtrees
Communications of the ACM
GESS: a scalable similarity-join algorithm for mining large data sets in high dimensional spaces
Proceedings of the seventh ACM SIGKDD international conference on Knowledge discovery and data mining
R-trees: a dynamic index structure for spatial searching
SIGMOD '84 Proceedings of the 1984 ACM SIGMOD international conference on Management of data
Spatial Searching in Geometric Databases
Proceedings of the Fourth International Conference on Data Engineering
The R-File: An Efficient Access Structure for Proximity Queries
Proceedings of the Sixth International Conference on Data Engineering
High Dimensional Similarity Search With Space Filling Curves
Proceedings of the 17th International Conference on Data Engineering
A Generic Approach to Bulk Loading Multidimensional Index Structures
VLDB '97 Proceedings of the 23rd International Conference on Very Large Data Bases
The R+-Tree: A Dynamic Index for Multi-Dimensional Objects
VLDB '87 Proceedings of the 13th International Conference on Very Large Data Bases
Filter Trees for Managing Spatial Data over a Range of Size Granularities
VLDB '96 Proceedings of the 22th International Conference on Very Large Data Bases
Efficient Bulk Operations on Dynamic R-trees
ALENEX '99 Selected papers from the International Workshop on Algorithm Engineering and Experimentation
Speeding up construction of PMR quadtree-based spatial indexes
The VLDB Journal — The International Journal on Very Large Data Bases
The quad-CIF tree: A data structure for hierarchical on-line algorithms
DAC '82 Proceedings of the 19th Design Automation Conference
Accurate Estimation of the Cost of Spatial Selections
ICDE '00 Proceedings of the 16th International Conference on Data Engineering
Data Redundancy and Duplicate Detection in Spatial Join Processing
ICDE '00 Proceedings of the 16th International Conference on Data Engineering
Hardware acceleration for spatial selections and joins
Proceedings of the 2003 ACM SIGMOD international conference on Management of data
Fast computation of database operations using graphics processors
SIGMOD '04 Proceedings of the 2004 ACM SIGMOD international conference on Management of data
Foundations of Multidimensional and Metric Data Structures (The Morgan Kaufmann Series in Computer Graphics and Geometric Modeling)
A Fast Similarity Join Algorithm Using Graphics Processing Units
ICDE '08 Proceedings of the 2008 IEEE 24th International Conference on Data Engineering
Database research in computer games
Proceedings of the 2009 ACM SIGMOD International Conference on Management of data
Indexing Moving Objects Using Short-Lived Throwaway Indexes
SSTD '09 Proceedings of the 11th International Symposium on Advances in Spatial and Temporal Databases
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Moving object databases arise in numerous applications such as traffic monitoring, crowd tracking, and games. They all require keeping track of objects that move and thus the database of objects must be constantly updated. The cover fieldtree (more commonly known as the loose quadtree and the loose octree, depending on the dimension of the underlying space) is designed to overcome the drawback of spatial data structures that associate objects with their minimum enclosing quadtree (octree) cells which is that the size of these cells depends more on the position of the objects and less on their size. In fact, the size of these cells may be as large as the entire space from which the objects are drawn. The loose quadtree (octree) overcomes this drawback by expanding the size of the space that is spanned by each quadtree (octree) cell c of width w by a cell expansion factor p (p0) so that the expanded cell is of width (1+p)*w and an object is associated with its minimum enclosing expanded quadtree (octree) cell. It is shown that for an object o with minimum bounding hypercube box b of radius r (i.e., half the length of a side of the hypercube), the maximum possible width w of the minimum enclosing expanded quadtree cell c is just a function of r and p, and is independent of the position of o. Normalizing w via division by 2r enables calculating the range of possible expanded quadtree cell sizes as a function of p. For p = 0.5 the range consists of just two values and usually just one value for p = 1. This makes updating very simple and fast as for p = 0.5, there are at most two possible new cells associated with the moved object and thus the update can be done in O(1) time. Experiments with random data showed that the update time to support motion in such an environment is minimized when p is infinitesimally less than 1, with as much as a one order of magnitude increase in the number of updates that can be handled vis-a-vis the p=0 case in a given unit of time. Similar results for updates were obtained for an N-body simulation where improved query performance and scalability were also observed. Finally, in order amplify the paper, a video tiled "Crates and Barrels" was produced which is an N-body simulation of 14,000 objects. The video is available from the following URL: http://www.youtube.com/watch?v=Sokq3FRGc0s. An applet to illustrate the behavior of the loose quadtree was developed and is available from http://donar.umiacs.umd. edu/quadtree/rectangles/loosequad.html.