Improved Randomized Selection Algorithm

Title: Improved Randomized Selection Algorithm

Research Question: Can the efficiency of the randomized selection algorithm be improved, and what are the implications for the average case and practical applications?

Methodology: The researchers proposed a simplified version of the Select algorithm that ignores some roundings. They analyzed its basic features and studied the average performance, high probability bounds, and practical rounded versions. They also implemented the algorithm and tested it on large inputs to assess its performance.

Results: The researchers showed that several versions of the improved Select algorithm require at most n+k+O(n1/2ln1/2n) comparisons on average and with high probability. This recapitulates the analysis of Floyd and Rivest and extends it to the case of non-distinct elements. Encouraging computational results on large median-finding problems were reported.

Implications: The improved Select algorithm competes with other methods in both theory and practice. It has a lower bound of 1.5n, leaving little room for improvement. The algorithm's average performance and practical rounded versions were studied, and future work should assess more fully the relative merits of these versions. The researchers also implemented the algorithm and tested it on large inputs, demonstrating its efficiency and effectiveness.

Conclusion: The improved randomized selection algorithm provides a significant advancement in the field, offering a more efficient method for finding the kth smallest element of a set. Its implications for average case performance and practical applications make it a valuable tool for researchers and practitioners alike.

Link to Article: https://arxiv.org/abs/0402005v1 Authors: arXiv ID: 0402005v1