A Dualheap Selection Algorithm - A Call for Analysis
<|reference_start|>A Dualheap Selection Algorithm - A Call for Analysis: An algorithm is presented that efficiently solves the selection problem: finding the k-th smallest member of a set. Relevant to a divide-and-conquer strategy, the algorithm also partitions a set into small and large valued subsets. Applied recursively, this partitioning results in a sorted set. The algorithm's applicability is therefore much broader than just the selection problem. The presented algorithm is based upon R.W. Floyd's 1964 algorithm that constructs a heap from the bottom-up. Empirically, the presented algorithm's performance appears competitive with the popular quickselect algorithm, a variant of C.A.R. Hoare's 1962 quicksort algorithm. Furthermore, constructing a heap from the bottom-up is an inherently parallel process (processors can work independently and simultaneously on subheap construction), suggesting a performance advantage with parallel implementations. Given the presented algorithm's broad applicability, simplicity, serial performance, and parallel nature, further study is warranted. Specifically, worst-case analysis is an important but still unsolved problem.<|reference_end|>
@article{sepesi2001a,
    title={A Dualheap Selection Algorithm - A Call for Analysis},
    author={Greg Sepesi},
    journal={arXiv preprint arXiv:cs/0103023},
    year={2001},
    archivePrefix={arXiv},
    eprint={cs/0103023},
    primaryClass={cs.DS cs.DC}
}