On the improvement of the in-place merge algorithm parallelization

TL;DR

This paper introduces new parallelization techniques for in-place merge algorithms, including median finding, data division strategies, and in-place swapping, resulting in significant speedups for large arrays.

Contribution

The paper proposes novel algorithms and strategies to improve parallel in-place merging, reducing data movement and enhancing speedup efficiency.

Findings

Significant speedup for arrays larger than 1000 elements

Effective in-place swapping with linear shifting algorithm

New median-finding algorithm for partitioning

Abstract

In this paper, we present several improvements in the parallelization of the in-place merge algorithm, which merges two contiguous sorted arrays into one with an O(T) space complexity (where T is the number of threads). The approach divides the two arrays into as many pairs of partitions as there are threads available; such that each thread can later merge a pair of partitions independently of the others. We extend the existing method by proposing a new algorithm to find the median of two partitions. Additionally, we provide a new strategy to divide the input arrays where we minimize the data movement, but at the cost of making this stage sequential. Finally, we provide the so-called linear shifting algorithm that swaps two partitions in-place with contiguous data access. We emphasize that our approach is straightforward to implement and that it can also be used for external (out of place) merging. The results demonstrate that it provides a significant speedup compared to sequential executions, when the size of the arrays is greater than a thousand elements.