# EGA: An Efficient GPU Accelerated Groupby Aggregation Algorithm
## 7 Conclusions  
This study addresses two critical challenges in GPU-accelerated GA: performance degradation under high hash table load factors (LF > 0.9) and the inability to process datasets exceeding GPU memory capacity. Through algorithmic innovation, we propose EGA--a dual-mode framework consisting of Single-Pass EGA (SP-EGA) for in-memory scenarios and Multi-Pass EGA (MP-EGA) for out-of-core computations. Three key advancements emerge:  
* Mechanism Design: SP-EGA reduces average probe distance by 60-95% compared to LPHGA through a two-phase hashing strategy (no-probe insertion followed by linear probing), achieving stable performance even at LF = 1.0. * Scalability Innovation: MP-EGA introduces a probabilistically guaranteed partitioning model based on \"balls-into-bins\" theory, combined with greedy merging and multi-stream pipelining, enabling efficient GA on datasets 50\(\times\) larger than GPU memory. * Performance Leap: Experimental validation demonstrates SP-EGA achieves 1.16-5.39\(\times\) speedup over SOTA hash-based GPU method LPHGA under high-LF scenarios and achieves 1.30-2.48\(\times\) speedup over SOTA sort-based GPU method cuDF, while MP-EGA outperforms CPU-based DuckDB by 6.45-29.12\(\times\) on billion-scale datasets. Our work redefines three paradigms in GPU-GA research: 1. Load Factor Tolerance: Challenges the long-standing \"LF \(\leq\) 0.5\" design rule, proving that high-density hash tables can maintain efficiency through probe optimization; 2. Heterogeneous Workflow: Establishes a CPU-GPU co-processing template using feedback-driven load balancing (\(LF_{\text{min}}/LF_{\text{max}}\) thresholds), reducing PCIe transfer overhead by 42% compared to static partitioning; 3. Algorithmic Generality: The probabilistic partition sizing model (Theorem 1) provides a mathematical foundation for out-of-core GPU algorithms beyond GA. Practically, EGA's latency reduction in billion-row aggregation (Figure 7) directly enables real-time analytics in the following: financial fraud detection systems requiring sub-second response on TB-scale transaction logs; IoT platforms processing high-velocity sensor data with strict SLAs; edge computing deployments where GPU resources are memory-constrained. While EGA significantly advances GPU-GA, two limitations open new research avenues:  
* Atomic Operation Dependency: The remaining 31.8% of non-overlapped computation time (Figure 8) stems from atomic synchronization. Future work will explore lock-free hashing using NVIDIA Hopper's thread block clusters. * Operator Extensibility: Although optimized for groupby aggregation, extending EGA's paradigm to JOIN and WINDOW functions could revolutionize GPU-based SQL engines--a direction we are actively pursuing. These advancements provide a robust solution for large-scale data analysis tasks, enabling real-time processing capabilities that are critical in domains such as finance, healthcare, and social media analytics. Looking ahead, future work will explore synchronization mechanisms beyond atomic instructions to further enhance performance, as well as extend our acceleration techniques to other big data operations, such as join operations, to broaden the applicability of GPU acceleration in data analysis. We provide our source code at [[https://github.com/PneNPproof/cpu_gpu_coprocess_groupby_agg](https://github.com/PneNPproof/cpu_gpu_coprocess_groupby_agg)]([https://github.com/PneNPproof/cpu_gpu_coprocess_groupby_agg](https://github.com/PneNPproof/cpu_gpu_coprocess_groupby_agg)) (accessed on 1 February 2025). Conceptualization, Z.W., and Y.S. ; methodology, Z.W. ; software, Z.W. ; validation, Z.W., Y.S., and Z.L. ; formal analysis, Z.W. ; investigation, Z.W., Y.S., and Z.L. ; resources, Z.W., Y.S., and Z.L. ; data curation, Z.W., Y.S., and Z.L. ; writing--original draft preparation, Z.W., Y.S., and Z.L. ; writing--review and editing, Z.W., Y.S., and Z.L. ; supervision, Y.S. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable.