Linked-Array Tournament Tree Sorting With Minimal Extra Memory
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Solution Overview
Problem
Existing sorting algorithms require significant additional memory resources, which can be inefficient and costly, especially in systems with limited memory capacity.
Innovation Solution
The implementation of a Linked-Array Tournament Tree (LATT) structure that utilizes a minimal amount of additional memory to sort data efficiently by swapping champion elements and updating node values, reducing memory requirements while maintaining sorting efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Quantity of substance
If traditional sorting algorithms are used, then data can be sorted, but significant additional memory resources are required
Solution Approach 1:
The patent implements a Linked-Array Tournament Tree (LATT) structure where the tournament tree is nested within the existing data array. The LATT uses the same memory space as the data array itself, with additional nodes shared across multiple arrays. This nesting approach allows the sorting structure to be contained within the data structure, eliminating the need for separate large memory allocations while maintaining efficient sorting capability through the tournament tree's hierarchical organization of elements.
Solution Approach 2:
The LATT structure serves multiple functions simultaneously: it acts as both the sorting structure and a space-efficient representation of the data. The tournament tree nodes serve as both comparison points for sorting and as organizational structures that enable in-place swapping operations. This multi-functionality reduces the overall memory footprint by eliminating redundant data structures that would traditionally be needed for sorting operations.
2Ease of operation
If additional memory is allocated for sorting, then sorting can be performed, but memory capacity is consumed
Solution Approach 1:
The patent performs preliminary actions by pre-establishing the LATT structure within the data array before sorting begins. The tournament tree is initialized using the existing data elements, and the linked-array structure is set up in advance. This preliminary setup allows the sorting process to proceed using only the existing memory space, as the necessary structural components are already in place and do not require additional memory allocation during execution.
Solution Approach 2:
The LATT acts as an intermediary structure that mediates between the data elements and the sorting operation. Rather than directly manipulating the data array during sorting, the LATT provides an intermediate representation that enables efficient in-place swaps and comparisons. This intermediary structure is built within the existing memory space and facilitates sorting operations without requiring separate large memory allocations for the sorting algorithm itself.
3Quantity of substance
If in-place sorting is implemented, then memory usage is reduced, but complex data structures are required
Solution Approach 1:
The patent segments the sorting problem into manageable portions through the hierarchical tournament tree structure. The LATT divides the data into multiple levels, with each level representing a stage of comparison and potential swapping. This segmentation allows the complex sorting operation to be broken down into simpler, systematic steps that can be implemented efficiently within the existing memory space, reducing the overall complexity burden while maintaining in-place operation.
Solution Approach 2:
The LATT structure is dynamic, allowing it to adapt during the sorting process through in-place swaps and updates. The linked-array connections can be modified as elements are swapped between the data array and the tournament tree nodes. This dynamic nature enables the structure to reconfigure itself during sorting operations, maintaining memory efficiency while providing the flexibility needed to handle complex sorting scenarios without requiring overly rigid or complex static data structures.
Data Source
AI summary
A system and method include receiving a plurality of elements in a data array to be sorted, assigning the elements a sequential index value, computing an amount of additional memory needed to sort the elements, creating a Linked-Array Tournament Tree (LATT), storing the LATT in the allocated amount of additional memory, initializing the LATT, initializing a number of iterations, initializing a next sorted index position in the data array, determining from the LATT, the index value of a champion element from all the winners of the pairwise comparisons, swapping the champion element with an element at the next sorted index position in the data array, updating the LATT responsive to the swapping, updating the next sorted index position, repeating a plurality of times, and outputting the data array having the elements in a sorted order.