HPC acceleration of large (min, +) matrix products to compute domination-type parameters in graphs
Department of Computer Sciences, Universidad de Almeria, Spain
arXiv:2409.17688 [cs.DM], (26 Sep 2024)
@article{Garz_n_2022,
title={HPC acceleration of large (min, +) matrix products to compute domination-type parameters in graphs},
volume={78},
ISSN={1573-0484},
url={http://dx.doi.org/10.1007/s11227-022-04574-5},
DOI={10.1007/s11227-022-04574-5},
number={16},
journal={The Journal of Supercomputing},
publisher={Springer Science and Business Media LLC},
author={Garzón, Ester M. and Martínez, José Antonio and Moreno, Juan José and Puertas, María Luz},
year={2022},
month={may},
pages={17826–17843}
}
The computation of the domination-type parameters is a challenging problem in Cartesian product graphs. We present an algorithmic method to compute the 2-domination number of the Cartesian product of a path with small order and any cycle, involving the (min,+) matrix product. We establish some theoretical results that provide the algorithms necessary to compute that parameter, and the main challenge to run such algorithms comes from the large size of the matrices used, which makes it necessary to improve the techniques to handle these objects. We analyze the performance of the algorithms on modern multicore CPUs and on GPUs and we show the advantages over the sequential implementation. The use of these platforms allows us to compute the 2-domination number of cylinders such that their paths have at most 12 vertices.
September 29, 2024 by hgpu
