In-Place Construction of Left-Balanced Point K-D Trees
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Solution Overview
Problem
Existing methods for constructing left-balanced and complete k-d trees require temporary data copies, which are memory-intensive and inefficient, especially for large data sets, as they necessitate constant rearrangement and use of additional memory for storing tree topology.
Innovation Solution
The method involves in-place construction techniques using heap-based and linear partitioning operations, allowing for the creation of left-balanced and complete k-d trees without requiring a copy of the input data, by rearranging points within the same memory buffer and utilizing heap structures or iterators to ensure balanced tree formation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If existing k-d tree construction algorithms are used, then the tree can be built with optimal O(N log N) run time complexity, but temporary data copies are required which increase memory requirements
Solution Approach 1:
The patent merges the input data array with the output k-d tree storage by performing in-place construction. The same memory buffer is used for both input points and the constructed tree, eliminating the need for separate temporary arrays. This is achieved through careful index management where the tree nodes are written directly into the input array positions.
Solution Approach 2:
The patent extracts the tree topology information from requiring separate storage by encoding it implicitly through the spatial arrangement of points. Instead of storing explicit parent-child pointers or structure metadata, the tree hierarchy is represented by the ordered arrangement of points in the array, with the root at position 0 and children positioned according to the binary space partitioning structure.
2Stability of the object's composition
If temporary data copies are used for construction, then the construction process can proceed with balanced tree formation, but additional memory buffers are required which reduce efficiency
Solution Approach 1:
The patent performs preliminary heapification of the input data before the main k-d tree construction process. By pre-organizing the data into a heap structure, the algorithm ensures that subsequent partitioning operations can proceed in-place while maintaining balance properties. This preliminary organization allows the construction to proceed efficiently without requiring additional buffering.
3Manufacturing precision
If constant re-arranging of particles is performed, then the tree structure can be built correctly, but two lists of particles are needed which increases memory usage
Solution Approach 1:
The patent transitions from a two-list approach (unprocessed and processed) to a single-list in-place approach by introducing dimensional indexing. Instead of moving elements between lists, the algorithm uses index calculations to access elements in their final positions within the same array, effectively adding a dimensional layer to the data organization that eliminates the need for duplicate storage.
Data Source
AI summary
Embodiments provide for a graphics processing apparatus including logic to receive data from an input buffer. The data can define a set of data points, where each data point includes one or more dimensions. The logic is configured to process the received data points to perform in-place construct a left-balanced and complete point k-d tree of the data points within the input buffer.