Multidimensional Histograms via Fuzzy Spatial Partitioning
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Solution Overview
Problem
Conventional heuristics for constructing histograms of spatial data, such as equi-area and equi-count techniques, often result in large or low-count partitions when dealing with complex spatial objects, leading to poor selectivity estimation and inefficient partitioning of multidimensional spaces.
Innovation Solution
The use of 'fuzzy' splitting techniques that allow a single spatial object to belong to multiple partitions, with weighted counting based on the object's overlap with each partition, and recursive partitioning that avoids subdividing partitions with low object counts, enabling more efficient partitioning and improved histogram construction.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional equi-area or equi-count heuristics are used to partition spatial data, then the partitioning process is simple and fast, but it creates large or low-count partitions that reduce selectivity estimation accuracy
Solution Approach 1:
The patent segments spatial objects into multiple weighted subobjects when a single object spans multiple partitions. This segmentation allows the object's contribution to be distributed across partitions proportionally to its overlap with each partition, rather than forcing the entire object into a single partition. This resolves the contradiction by enabling more accurate selectivity estimation through proper object distribution while maintaining computational feasibility through the weighted counting mechanism.
Solution Approach 2:
The patent changes the counting parameter from binary (object either in partition or not) to weighted (object contributes fractionally to multiple partitions based on overlap). This parameter change transforms the partitioning approach from simple equi-area/equi-count methods to a more nuanced weighted counting system that accurately reflects spatial relationships, thereby improving selectivity estimation without requiring complex partition boundaries.
2Productivity
If a single spatial object is assigned to only one partition, then the partitioning is simple, but it creates large partitions when objects span multiple areas and reduces histogram utility
Solution Approach 1:
The patent introduces weighted subobjects as an intermediary mechanism between spatial objects and partitions. Instead of directly assigning entire objects to single partitions, the system creates weighted subobjects that represent the object's presence in multiple partitions with appropriate weights. This intermediary approach maintains histogram construction efficiency while improving selectivity estimation reliability by accurately capturing spatial overlaps.
Solution Approach 2:
The patent adds a weighting dimension to the traditional partitioning approach. Rather than simply assigning objects to partitions based on spatial location alone, the system introduces a weight dimension that quantifies the degree of overlap between objects and partitions. This additional dimension enables more accurate selectivity estimation while maintaining the efficiency of histogram-based query optimization.
3Measurement precision
If partitions are recursively subdivided to achieve equal object distribution, then equi-count histograms are formed, but this creates many small partitions with low object counts that reduce estimation accuracy
Solution Approach 1:
The patent replaces the mechanical recursive subdivision process with a weighted counting approach. Instead of repeatedly dividing partitions to achieve equal object distribution, the system uses weighted subobjects to accurately count object contributions in each partition. This substitution eliminates the creation of many small, low-count partitions while maintaining precise selectivity estimation through the weighted counting mechanism.
Data Source
AI summary
Techniques are described for generating histograms for a multidimensional space. In the presence of large spatial objects, fuzzy splitting techniques are utilized to recursively divide the multidimensional space into partitions, where a single spatial object may belong to multiple partitions. Large spatial objects are essentially broken down into smaller objects that may allow for more efficient partitioning of the multidimensional space. A count of spatial objects in each partition yields a spatial histogram. A spatial object that belongs to multiple partitions may have a weighted count for each of the multiple partitions, based on the extent to which the spatial object overlaps with each partition. Thus, an object that is split among a handful of partitions will only contribute a fraction of a count to each partition. Small partitions having relatively few objects are avoided by refusing to subdivide a partition whose members drop below a threshold number.