Spatial query processing in an object-oriented database system
SIGMOD '86 Proceedings of the 1986 ACM SIGMOD international conference on Management of data
Redundancy in spatial databases
SIGMOD '89 Proceedings of the 1989 ACM SIGMOD international conference on Management of data
Applications of random sampling in computational geometry, II
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
Multi-step processing of spatial joins
SIGMOD '94 Proceedings of the 1994 ACM SIGMOD international conference on Management of data
An optimal algorithm for finding segments intersections
Proceedings of the eleventh annual symposium on Computational geometry
SIGMOD '96 Proceedings of the 1996 ACM SIGMOD international conference on Management of data
Partition based spatial-merge join
SIGMOD '96 Proceedings of the 1996 ACM SIGMOD international conference on Management of data
On two-dimensional indexability and optimal range search indexing
PODS '99 Proceedings of the eighteenth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Constraint Databases
PROBE Spatial Data Modeling and Query Processing in an Image Database Application
IEEE Transactions on Software Engineering
Proceedings of the Seventh International Conference on Data Engineering
A New Algorithm for Computing Joins with Grid Files
Proceedings of the Ninth International Conference on Data Engineering
Efficient Computation of Spatial Joins
Proceedings of the Ninth International Conference on Data Engineering
Parallel Processing of Spatial Joins Using R-trees
ICDE '96 Proceedings of the Twelfth International Conference on Data Engineering
Spatial Joins Using R-trees: Breadth-First Traversal with Global Optimizations
VLDB '97 Proceedings of the 23rd International Conference on Very Large Data Bases
A Raster Approximation For Processing of Spatial Joins
VLDB '98 Proceedings of the 24rd International Conference on Very Large Data Bases
Scalable Sweeping-Based Spatial Join
VLDB '98 Proceedings of the 24rd International Conference on Very Large Data Bases
Extending Rectangle Join Algorithms for Rectilinear Polygons
WAIM '00 Proceedings of the First International Conference on Web-Age Information Management
Counting and Reporting Red/Blue Segment Intersections
WADS '93 Proceedings of the Third Workshop on Algorithms and Data Structures
The Buffer Tree: A New Technique for Optimal I/O-Algorithms (Extended Abstract)
WADS '95 Proceedings of the 4th International Workshop on Algorithms and Data Structures
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
ESA '95 Proceedings of the Third Annual European Symposium on Algorithms
An Index Structure for Spatial Joins in Linear Constraint Databases
ICDE '99 Proceedings of the 15th International Conference on Data Engineering
Algorithms for Reporting and Counting Geometric Intersections
IEEE Transactions on Computers
Geometric intersection problems
SFCS '76 Proceedings of the 17th Annual Symposium on Foundations of Computer Science
A fast planar partition algorithm. I
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
An optimal algorithm for intersecting line segments in the plane
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
Experimental evaluation of filter effectiveness (extended abstract)
Proceedings of the 8th ACM international symposium on Advances in geographic information systems
Trajectory queries and octagons in moving object databases
Proceedings of the eleventh international conference on Information and knowledge management
On Multi-way Spatial Joins with Direction Predicates
SSTD '01 Proceedings of the 7th International Symposium on Advances in Spatial and Temporal Databases
Filtering with raster signatures
GIS '06 Proceedings of the 14th annual ACM international symposium on Advances in geographic information systems
ACM Transactions on Database Systems (TODS)
Estimating the overlapping area of polygon join
SSTD'05 Proceedings of the 9th international conference on Advances in Spatial and Temporal Databases
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Efficient evaluation of spatial join is an important issue in spatial databases. The traditional evaluation strategy is to perform a join of 驴minimum bounding rectangles驴 (MBR) of the spatial objects (MBR-filter) and evaluate the actual join of the objects using the results of the join on approximations. Improvements to add additional filtering using approximations that are more accurate were also considered.In the present paper, we develop efficient algorithms for evaluating joins of 驴trapezoids驴 without using MBR's. For the case where there are no intersecting non-horizontal boundaries of trapezoids in the same set, a spatial join of two sets of N trapezoids can be evaluated in O(Nlogb N+k) I/Os, where b is the page size and k the number of trapezoid intersections. For the general case without any assumptions, a join can be done in O((N+l+k)logb N) I/Os, where l is the total number of intersections of non-horizontal boundaries within the same set, and N,k,b are the same as above.The new algorithms can be used to evaluate spatial joins for polygons. One possibility is to decompose polygons into trapezoids and apply a trapezoid join algorithm. In particular, this approach is efficient for 驴I/O bounded polygons驴 (each of which can be retrieved in a constant number of I/Os). Given two sets of N I/O bounded polygons, we show that in the case where there are no boundary intersections among polygons of the same set, the join of the two sets can be computed in O(Nlogb N+k) I/Os, and in the case where there is no such assumption, the join takes O((N+l+k)logb N) I/Os, where b is the page size, k the number of pairs of intersecting polygons, and l the number of boundary intersections within the same polygon set. Another possibility is to approximate objects by I/O bounded polygons (e.g., 5-corner convex polygons), which are finer than rectangles and use the new algorithms as a filter.