Efficient Selection Algorithm for Nondistinct Elements: Difference between revisions
Created page with "Title: Efficient Selection Algorithm for Nondistinct Elements Abstract: This research article presents an improved version of the selection algorithm known as Select, originally proposed by Floyd and Rivest in 1975. The algorithm is used to find the kth smallest element in a set of n elements, with nondistinct elements. The main contribution of this research is the analysis of the algorithm, showing that it requires at most n + min {k, n - k} + O(n^2/3 ln 1/3 n) compari..." |
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Title: Efficient Selection Algorithm for Nondistinct Elements | Title: Efficient Selection Algorithm for Nondistinct Elements | ||
Abstract: This research article presents an improved version of the | Abstract: This research article presents an improved version of the Select algorithm for finding the kth smallest element in a set of n elements, even when those elements are not distinct. The algorithm uses a randomized selection method with quintary partitions, which significantly reduces the average number of comparisons needed to find the kth smallest element. The results show that the Select algorithm can be more efficient than other existing methods, making it a potentially better choice for practical applications. | ||
Main Research Question: Can | Main Research Question: Can the Select algorithm be improved to work more efficiently with nondistinct elements? | ||
Methodology: The | Methodology: The study uses a randomized selection method with quintary partitions, which involves dividing the set of elements into five subsets based on their values. This method is applied to the Select algorithm to reduce the number of comparisons needed to find the kth smallest element. | ||
Results: The | Results: The research shows that the improved Select algorithm requires at most n + min {k, n - k} + O(n^2/3 ln^1/3 n) comparisons on average. This result agrees with the previous analysis of the Select algorithm, which was based on an unproven assumption. The study also proves that non-recursive versions of the Select algorithm, which use other selection or sorting algorithms for smaller subproblems, require at most n + min {k, n - k} + o(n) comparisons with high probability. | ||
Implications: The improved | Implications: The improved Select algorithm presented in this study has significant implications for practical applications. It offers a more efficient method for finding the kth smallest element in a set of n elements, even when those elements are not distinct. This could lead to faster implementation of the algorithm in various applications, such as sorting and finding convex hulls. | ||
Keywords: Selection algorithm, nondistinct elements, quintary partitions, computational complexity | |||
Link to Article: https://arxiv.org/abs/ | Link to Article: https://arxiv.org/abs/0312055v1 | ||
Authors: | Authors: | ||
arXiv ID: | arXiv ID: 0312055v1 | ||
[[Category:Computer Science]] | [[Category:Computer Science]] | ||
[[Category:Algorithm]] | |||
[[Category:N]] | [[Category:N]] | ||
[[Category:Elements]] | [[Category:Elements]] | ||
[[Category:Select]] | [[Category:Select]] | ||
[[Category:Selection]] |
Latest revision as of 15:09, 24 December 2023
Title: Efficient Selection Algorithm for Nondistinct Elements
Abstract: This research article presents an improved version of the Select algorithm for finding the kth smallest element in a set of n elements, even when those elements are not distinct. The algorithm uses a randomized selection method with quintary partitions, which significantly reduces the average number of comparisons needed to find the kth smallest element. The results show that the Select algorithm can be more efficient than other existing methods, making it a potentially better choice for practical applications.
Main Research Question: Can the Select algorithm be improved to work more efficiently with nondistinct elements?
Methodology: The study uses a randomized selection method with quintary partitions, which involves dividing the set of elements into five subsets based on their values. This method is applied to the Select algorithm to reduce the number of comparisons needed to find the kth smallest element.
Results: The research shows that the improved Select algorithm requires at most n + min {k, n - k} + O(n^2/3 ln^1/3 n) comparisons on average. This result agrees with the previous analysis of the Select algorithm, which was based on an unproven assumption. The study also proves that non-recursive versions of the Select algorithm, which use other selection or sorting algorithms for smaller subproblems, require at most n + min {k, n - k} + o(n) comparisons with high probability.
Implications: The improved Select algorithm presented in this study has significant implications for practical applications. It offers a more efficient method for finding the kth smallest element in a set of n elements, even when those elements are not distinct. This could lead to faster implementation of the algorithm in various applications, such as sorting and finding convex hulls.
Keywords: Selection algorithm, nondistinct elements, quintary partitions, computational complexity
Link to Article: https://arxiv.org/abs/0312055v1 Authors: arXiv ID: 0312055v1