A Dualheap Selection Algorithm - A Call for Analysis

TL;DR

This paper introduces a dualheap selection algorithm that efficiently finds the k-th smallest element, partitions sets, and has potential advantages in parallel processing, with broad applicability beyond selection problems.

Contribution

It presents a novel dualheap algorithm based on Floyd's heap construction, offering a competitive, simple, and parallelizable alternative to existing selection methods.

Findings

Performance competitive with quickselect

Parallel heap construction possible

Broad applicability beyond selection

Abstract

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.