# Efficiently Computing Maximum Clique of Sparse Graphs with Many-Core Graphical Processing Units

### Lorenzo Cardone, Salvatore Di Martino, Stefano Quer

#### 2024

#### Abstract

The Maximum Clique is a fundamental problem in graph theory and has numerous applications in various domains. The problem is known to be NP-hard, and even the most efficient algorithm requires significant computational resources when applied to medium or large graphs. To obtain substantial acceleration and improve scalability, we enable highly parallel computations by proposing a many-core graphical processing unit implementation targeting large and sparse real-world graphs. We developed our algorithm from CPU-based solvers, redesigned the graph preprocessing step, introduced an alternative parallelization scheme, and implemented block-level and warp-level parallelism. We show that the latter performs better when the amount of threads included in a block cannot be fully exploited. We analyze the advantages and disadvantages of the proposed strategy and its behavior on different graph topologies. Our approach, applied to sparse real-world graph instances, shows a geomean speed-up of 9x, an average speed-up of over 19x, and a peak speed-up of over 70x, compared to a parallel implementation of the BBMCSP algorithm. It also obtains a geometric mean speed-up of 1.21x and an average speed-up of over 2.0x on the same graph instances compared to the parallel implementation of the LMC algorithm.

Download#### Paper Citation

#### in Harvard Style

Cardone L., Di Martino S. and Quer S. (2024). **Efficiently Computing Maximum Clique of Sparse Graphs with Many-Core Graphical Processing Units**. In *Proceedings of the 19th International Conference on Software Technologies - Volume 1: ICSOFT*; ISBN 978-989-758-706-1, SciTePress, pages 539-546. DOI: 10.5220/0012852700003753

#### in Bibtex Style

@conference{icsoft24,

author={Lorenzo Cardone and Salvatore Di Martino and Stefano Quer},

title={Efficiently Computing Maximum Clique of Sparse Graphs with Many-Core Graphical Processing Units},

booktitle={Proceedings of the 19th International Conference on Software Technologies - Volume 1: ICSOFT},

year={2024},

pages={539-546},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0012852700003753},

isbn={978-989-758-706-1},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 19th International Conference on Software Technologies - Volume 1: ICSOFT

TI - Efficiently Computing Maximum Clique of Sparse Graphs with Many-Core Graphical Processing Units

SN - 978-989-758-706-1

AU - Cardone L.

AU - Di Martino S.

AU - Quer S.

PY - 2024

SP - 539

EP - 546

DO - 10.5220/0012852700003753

PB - SciTePress