一个双堆选择算法--需要分析
A Dualheap Selection Algorithm - A Call for Analysis
摘要：
提出了一种算法，有效地解决了选择问题：找到一个集合的第k个最小的成员。与分治策略相关，该算法还将集合划分为小值子集和大值子集。递归地应用，这种划分会产生一个有序集。因此，该算法的适用性比选择问题更广泛。该算法基于R.W. Floyd的1964年算法，自底向上构造堆。从经验来看，所提出的算法的性能似乎与流行的快速选择算法（C.A.R.的变体）具有竞争力1962年霍尔的快速排序算法。此外，自底向上构造堆是一个固有的并行过程（处理器可以独立地同时进行子堆构造），这表明并行实现具有性能优势。鉴于所提出的算法的广泛适用性，简单，串行性能，并行性质，进一步的研究是必要的。具体而言，最坏情况分析是一个重要但尚未解决的问题。
英文摘要：
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.
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