Spatial Search Using Key-Value Store and Space-Filling Curves
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Solution Overview
Problem
Existing spatial search methods become inefficient when dealing with large-scale geometry storage and partitioning, as brute-force approaches are not scalable for numerous defined geometric shapes.
Innovation Solution
The use of a key-value store with deterministic space division and space-filling curves to decompose geometric shapes into spatial cells, enabling efficient traversal and querying of search spaces.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If brute-force approaches are used for geometry search, then simplicity of implementation is maintained, but search efficiency deteriorates at large scale
Solution Approach 1:
The patent segments the search space into hierarchical levels using space-filling curves (e.g., Hilbert curves), dividing the geometric space into cells at different resolution levels. This segmentation allows the search algorithm to traverse only relevant portions of the space rather than checking all geometries, thereby improving search efficiency while maintaining implementation feasibility through systematic division.
Solution Approach 2:
The patent transforms the multi-dimensional geometric search problem into a one-dimensional traversal problem by mapping spatial coordinates to a single dimension using space-filling curves. This dimensionality change enables efficient linear traversal of spatial cells while preserving spatial locality, resolving the contradiction between implementation simplicity and search efficiency.
2Quantity of substance
If large scale geometry storage is implemented, then spatial search capability is improved, but computational complexity increases
Solution Approach 1:
The patent divides the large-scale geometry storage into hierarchical spatial cells organized by resolution levels. Each geometry is associated with cells at multiple levels, allowing the system to manage large quantities of geometries by organizing them in a structured hierarchy rather than storing them as unstructured data, thereby reducing computational complexity for search operations.
Solution Approach 2:
The patent performs preliminary spatial indexing by pre-computing and storing the hierarchical cell representations for all geometries before search operations. This preliminary action organizes the geometry data into an efficient spatial structure, reducing the computational complexity during actual search operations even as the quantity of stored geometries increases.
3Productivity
If spatial partitioning is performed, then search performance is improved, but data structure complexity increases
Solution Approach 1:
The patent uses space-filling curves to transform multi-dimensional spatial partitioning into a one-dimensional hierarchical structure. This approach maintains the spatial relationships needed for efficient search performance while simplifying the data structure to a linear hierarchy of cells, reducing the apparent complexity compared to traditional multi-dimensional spatial indexes.
Solution Approach 2:
The hierarchical spatial cell structure serves multiple functions simultaneously: it enables efficient spatial search, supports large-scale geometry storage, and provides a unified data structure that can handle various types of geometric queries. This multi-functionality reduces the need for separate complex data structures for different search operations.
Data Source
AI summary
A spatial search may be performed using representations of geometric shapes stored in a key-value store. A request to perform a spatial search may be received, the request including a geometric shape composed of one or more points. The points of the geometrical shape may be translated into one or more spatial indexes representing spatial cells using a space-filling curve. A key-value store may then be incrementally searched for each spatial index to identify spatial cells intersecting the geometric shape for which other known geometric shapes exist. The key-value store may then be searched to identify the known geometric shapes intersecting the geometric shape included in the search.