Linear-Time Top-K Sort Using Min-Heap Extraction
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Solution Overview
Problem
Conventional sort algorithms, such as heap sort, have an O(n log n) time complexity, making it inefficient to retrieve top-k results in linear time, which is necessary for processing vast amounts of data in applications like Web search and distributed systems.
Innovation Solution
A linear-time top-k sort method using a min or max heap structure that compares new data elements with the root node and readjusts the heap to maintain candidate top-k results, achieving O(n) time complexity by constructing and reconstructing the heap with k elements and extracting k elements in linear time.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If conventional sort algorithms (heap sort, merge sort, quick sort) are used to retrieve top-k results, then the results are obtained in sorted order, but the time complexity is O(n log n) which is inefficient for large datasets
Solution Approach 1:
The invention extracts only the necessary k elements from the dataset using a heap structure of size k, rather than sorting all n elements. By maintaining a heap of size k and comparing new elements with the root, the algorithm extracts only the top-k results without performing full sorting, achieving O(n) time complexity instead of O(n log n).
Solution Approach 2:
The algorithm performs partial sorting by maintaining a heap of size k rather than sorting the entire dataset of size n. This partial action (sorting only k elements at any time) is sufficient to obtain top-k results, reducing the computational work from O(n log n) to O(n) while still achieving the desired sorted output for the top-k elements.
2Manufacturing precision
If full sorting is performed on n data elements, then all elements are arranged in sorted order, but the storage space required is proportional to the dataset size n
Solution Approach 1:
The invention extracts and maintains only k elements in the heap structure at any time, rather than storing and sorting all n elements. This extraction approach ensures that only the necessary top-k elements are kept in memory in sorted order, reducing storage space from O(n) to O(k) while maintaining the accuracy of sorted ordering for the results.
Data Source
AI summary
The present invention relates to an algorithm that retrieves only k data elements having the largest (or smallest) key values from a dataset (i.e., top-k results) in a time linearly proportional to the size of the dataset. The proposed method using the algorithm finds the top-k results using a k-sized min (or max) heap structure that maintains candidate elements of the top-k results by scanning all data elements in the dataset only once. In other words, the present invention provides a linear-time top-k sort method that finds top-k results in a time linearly proportional to the size of the dataset (i.e., O(n) time complexity), while conventional sort algorithms for finding top-k results cannot find the top-k results in a time linearly proportional to the size of the dataset (i.e., at least O(n log n) time complexity).