# Mapping Hex-Cells into Two-Dimension Mesh Network

### Abdulelah Saif

#### Abstract

Graph mapping is an important aspect for interconnection networks used for communication between processors in parallel systems. Some parallel algorithms use communication structures which can be represented by Hex-Cells HC. In order to run these algorithms on Two-Dimension 2D Mesh multiprocessor system, without changing the current topology and the running application, their communication graphs need to be embedded into 2D mesh. In this paper, we have developed an algorithm for embedding Hex-Cells HC(i) into 2D mesh M(2i,4i-1), where i = 1,2,3,.....i.e. To measure the efficiency of the algorithm, a comparison is done between 2D Mesh and Tree-hypercube in terms of dilation, congestion and expansion. As a result, the embedding of Hex-cells into 2D Mesh has dilation 1, congestion 1, expansion (4i-1)/3i, where i is the level of HC which is better than Tree-hypercube. Moreover, 2D Mesh embeds hex-cells for any level whereas Tree-hypercube embeds hex-cells for two levels.

Download#### Paper Citation

#### in Harvard Style

Saif A. (2020). **Mapping Hex-Cells into Two-Dimension Mesh Network**.In *Proceedings of the 1st International Conference on Computing and Emerging Sciences - Volume 1: ICCES,* ISBN 978-989-758-497-8, pages 27-35. DOI: 10.5220/0010374300270035

#### in Bibtex Style

@conference{icces20,

author={Abdulelah Saif},

title={Mapping Hex-Cells into Two-Dimension Mesh Network},

booktitle={Proceedings of the 1st International Conference on Computing and Emerging Sciences - Volume 1: ICCES,},

year={2020},

pages={27-35},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0010374300270035},

isbn={978-989-758-497-8},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 1st International Conference on Computing and Emerging Sciences - Volume 1: ICCES,

TI - Mapping Hex-Cells into Two-Dimension Mesh Network

SN - 978-989-758-497-8

AU - Saif A.

PY - 2020

SP - 27

EP - 35

DO - 10.5220/0010374300270035