In-Memory R-tree Spatial Query Processing
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Solution Overview
Problem
Existing spatial query systems face performance issues when processing topological relationships between complex spatial objects due to large numbers of test geometries and high complexity, leading to inefficient query processing times.
Innovation Solution
The implementation of In-Memory R-tree (IMR-tree) techniques for filtering and refining steps in spatial query processing, which supports various geometries like polygons, points, and lines, and optimizes the 9-intersection matrix calculations to determine spatial relationships between query and test objects.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If sweep line based algorithm is used to process topological queries, then the query can be performed systematically, but the query performance deteriorates due to large number of test geometries and high complexity
Solution Approach 1:
The patent segments the continuous sweep line algorithm into discrete spatial index-based operations. The query space is divided into manageable regions using spatial indexes (R-trees, quad-trees), and topological relationships are determined by examining intersections at discrete index nodes rather than continuously sweeping through all geometries. This segmentation reduces the computational complexity from O(n²) to approximately O(n log n) by organizing geometries into hierarchical spatial structures.
Solution Approach 2:
The patent performs preliminary actions by pre-building spatial indexes on the test geometries before query execution. The spatial index structures (R-trees, quad-trees) are constructed in advance to organize geometries by their minimum bounding rectangles (MBRs). During query processing, these pre-built indexes enable rapid filtering of candidate geometries that could potentially intersect with the query geometry, eliminating the need to check all geometries systematically as in the traditional sweep line approach.
2Productivity
If spatial index with filtering and refinement steps is used, then query performance improves for large number of test geometries, but the processing complexity increases due to multiple processing steps
Solution Approach 1:
The patent merges the filtering and refinement steps into a unified hierarchical processing framework. The spatial index structure combines both functions: the upper levels of the index tree perform filtering by eliminating geometries that cannot possibly intersect, while lower levels perform refinement by precisely determining topological relationships. This merging eliminates the need for separate sequential processing steps, reducing overall processing complexity while maintaining the performance benefits of both filtering and refinement.
Solution Approach 2:
The patent introduces minimum bounding rectangles (MBRs) as intermediary objects that facilitate efficient filtering. MBRs serve as simplified proxies for complex geometries during the filtering phase, enabling rapid spatial comparisons without dealing with the full geometric complexity. The MBR intersection tests act as an intermediary step that quickly identifies candidate geometries for more detailed topological analysis, bridging the gap between simple spatial filtering and complex topological relationship determination.
3Productivity
If interior approximation and TR*-tree are used for complex geometries, then query performance improves, but the system complexity increases due to additional data structures
Solution Approach 1:
The patent applies parameter changes by transforming complex geometries into simplified representations with modified parameters. Complex polygons are decomposed into simpler geometric primitives (triangles, quadrilaterals) with well-defined topological properties. The query processing then operates on these simplified representations using standardized topological relationship definitions, avoiding the need for complex interior approximation algorithms while maintaining query accuracy.
Solution Approach 2:
The patent implements a universal spatial index framework that handles multiple geometry types (points, lines, polygons, multi-polygons) and all topological relationships (disjoint, touch, intersect, contain, inside) through a single unified data structure. The R-tree and quad-tree structures are designed to be geometry-type agnostic, accommodating various spatial objects and relationships without requiring separate specialized data structures for each geometry type or relationship type.
Data Source
AI summary
An optimized method of processing queries requesting a description of a spatial relationship between a test geometry and a query geometry, such as points, lines, polygons, and collections thereof, is disclosed. A first part of the method finds a first spatial relationship between a minimum bounding rectangle (MBR) of the test geometry and an In-Memory R-tree (IMR-tree) built to describe the query geometry. If the first relationship does not specify the requested description, then a second part of the method uses the IMR-tree of the query geometry to find a second spatial relationship between the test geometry itself and the query geometry. Optimizations are applied to the first part and to the second part. Optimizations in the second part depend on the test geometry.