Dualheap Selection Algorithm: Efficient, Inherently Parallel and Somewhat Mysterious

TL;DR

The paper introduces a parallel selection algorithm called dualheap selection, which, despite limited novelty, offers efficient and balanced performance on parallel processors, outperforming traditional quickselect methods.

Contribution

The paper presents a dualheap selection algorithm with minor implementation innovations that enable efficient parallel execution and balanced workload distribution.

Findings

Competitive performance with quickselect on single processors

Superior scalability and efficiency on parallel processors

Easily partitioned and balanced subtasks for parallel execution

Abstract

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.