arXiv subjects
Publications and source records attributed to Greg Sepesi.
A generalization of the heapsort algorithm is proposed. At the expense of about 50% more comparison and move operations for typical cases, the dualheap sort algorithm offers several advantages over heapsort: improved cache performance, better performance if the input happens to be already sorted, and easier parallel implementations.
An inherently parallel algorithm is proposed that efficiently performs selection: finding the K-th largest member of a set of N members. Selection is a common component of many more complex algorithms and therefore is a widely studied problem. Not much is new in the proposed dualheap selection algorithm: the heap data structure is from J.W.J.Williams, the bottom-up heap construction is from R.W. Floyd, and the concept of a two heap data structure is from J.W.J. Williams and D.E. Knuth. The algorithm's novelty is limited to a few relatively minor implementation twists: 1) the two heaps are oriented with their roots at the partition values rather than at the minimum and maximum values, 2)the coding of one of the heaps (the heap of smaller values) employs negative indexing, and 3) the exchange phase of the algorithm is similar to a bottom-up heap construction, but navigates the heap with a post-order tree traversal. When run on a single processor, the dualheap selection algorithm's performance is competitive with quickselect with median estimation, a common variant of C.A.R. Hoare's quicksort algorithm. When run on parallel processors, the dualheap selection algorithm is superior due to its subtasks that are easily partitioned and innately balanced.
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.