K-Element Selection via Section Threshold Partitioning
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Solution Overview
Problem
Existing methods for selecting the K greatest or least numbers from a list of N elements require significant data manipulation through sorting, where much of the sorting is wasteful as it does not contribute to the selection of the K elements.
Innovation Solution
A computer-implemented method that partitions the list into sections, iteratively determines section thresholds, and uses these thresholds to select the K greatest or least elements efficiently by leveraging SIMD processing and instructional level parallelism, reducing unnecessary operations through decoupling data entries and parallel processing.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If complete sorting is used to select K greatest elements, then selection accuracy is improved, but computational complexity increases
Solution Approach 1:
The patent divides the N-element list into multiple sections (e.g., first section, second section, third section) and processes each section separately to identify threshold values. This segmentation allows the algorithm to avoid complete sorting while still achieving accurate K-element selection by comparing sections against dynamically adjusted thresholds.
Solution Approach 2:
The patent performs preliminary processing by partitioning the list into sections and pre-calculating threshold values for each section before the final selection. This preliminary action reduces the computational burden of the main selection process by eliminating elements that cannot possibly be in the top K.
2Measurement precision
If complete sorting is performed, then all K greatest elements are correctly identified, but processing time increases
Solution Approach 1:
The patent performs only the necessary portion of sorting by processing sections separately and using threshold-based filtering. Instead of completely sorting all N elements, it applies partial sorting within sections and uses threshold comparisons to eliminate unnecessary elements, significantly reducing processing time while maintaining accuracy.
Solution Approach 2:
The patent extracts and processes only the relevant portions of the data by dividing the list into sections and focusing computational effort on identifying threshold values for each section. This extraction approach avoids the time cost of sorting entire datasets while still achieving correct K-element selection.
3Productivity
If section-based threshold comparison is used, then computational overhead is reduced, but algorithm complexity increases
Solution Approach 1:
The patent segments the data processing into distinct phases: partitioning the list into sections, calculating threshold values for each section, comparing elements against thresholds, and performing final selection. This structured segmentation makes the algorithm more manageable and implementable despite the increased complexity compared to simple sorting.
Data Source
AI summary
A computer implemented method selects K extreme elements of a list of N elements by partitioning each of the N elements into a plurality of sections. For each section the method selects a threshold selection determining at least K extreme entries from the list. This iteratively compares a corresponding section to a section threshold, counts a number of sections which are more extreme than the section threshold, increasing (or decreasing) the section threshold if the count is greater than K and decreasing (or increasing) the section threshold if the count is less than K. The method forms a combined threshold by concatenation of said section thresholds in order, compares each of the N elements to the combined threshold, and selects at least K elements from the set of N elements more extreme than the combined threshold.