# Stable Minimum Storage Merging by Symmetric Comparisons

@inproceedings{Kim2004StableMS, title={Stable Minimum Storage Merging by Symmetric Comparisons}, author={Pok-Son Kim and Arne Kutzner}, booktitle={ESA}, year={2004} }

We introduce a new stable minimum storage algorithm for merging that needs \(O(m\log(\frac{n}{m}+1))\) element comparisons, where m and n are the sizes of the input sequences with m≤ n. According to the lower bound for merging, our algorithm is asymptotically optimal regarding the number of comparisons.

## 14 Citations

A Simple Algorithm for Stable Minimum Storage Merging

- Computer ScienceSOFSEM
- 2007

A principle of symmetric splitting is presented, where the start and end point of a rotation are computed by a repeated halving of two search spaces, which is structurally simpler than the principle of asymmetric comparisons introduced earlier by Kim and Kutzner.

On Optimal and Efficient in Place Merging

- Computer ScienceSOFSEM
- 2006

A new stable in place merging algorithm that needs O(mlog$(\frac{n}{m}+1) comparisons and O(m+n) assignments and according to the lower bounds for merging is asymptotically optimal regarding the number of comparisons as well as assignments.

On a Simple and Stable Merging Algorithm

- Computer Science
- 2010

This work investigates the worst case complexity regarding the number of comparisons for a simple and stable merging algorithm and gives a transparent solution for the hardly tractable problem of delivering a clean complexity analysis for the algorithm.

DuelMerge: Merging with Fewer Moves

- Computer ScienceComput. J.
- 2017

This work proposes DUELMERGE, a stable merging algorithm that is asymptotically optimal in the number of comparisons and performs ( ( ( )) O n n log2 moves), which performs fewer moves than other stable solutions.

Lazy-Merge: A Novel Implementation for Indexed Parallel K-Way In-Place Merging

- Computer ScienceIEEE Trans. Parallel Distributed Syst.
- 2016

This research proposes Lazy-Merge, a novel implementation of sequential in- place in-place merging algorithms, that can be utilized in their parallel counterparts and compared with the existing algorithms on number of moves and execution time.

Asymptotically Optimal Merging on ManyCore GPUs

- Computer ScienceIEICE Trans. Inf. Syst.
- 2012

The asymptotic optimality of the splitting process is formally proved and it is shown that for symmetrically sized inputs the authors' approach delivers up to 4 times faster runtimes than the thrust::merge function that is part of the Thrust library.

A Time-space Efficient Algorithm for Parallel k-way In-place Merging based on Sequence Partitioning and Perfect Shuffle

- Computer Science
- 2020

The huge data volumes, big data, and the emergence of new parallel architectures lead to revisiting classic computer science topics and the motivation of the proposed work for revisiting the parallel architectures is motivated by the desire to revisit these topics.

A Time-space Efficient Algorithm for Parallel k-way In-place Merging based on Sequence Partitioning and Perfect Shuffle

- Computer ScienceACM Trans. Parallel Comput.
- 2020

To evaluate the proposed algorithm, as PS-merge produces the standard merging format, this algorithm is compared against the state-of-the-art methods, bitonic merge, a parallel binary merge tree, and lazy-MERge to show a significant improvement in overall execution time.

EMS: AN ENHANCEDMERGE SORT ALGORITHMBY EARLY CHECKING OF ALREADY SORTED PARTS

- Computer ScienceInternational Journal of Software Engineering and Computer Systems
- 2019

A modified version of merge sort is given, which in practice shows substantial improvement in running time than the top-down and bottom-up implementations of the classical merge sort.

In-place permuting and perfect shuffling using involutions

- Mathematics, Computer ScienceInf. Process. Lett.
- 2013

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