GPU-Parallel Gabriel Graph Construction: Up to 8484x Speedup
ORIGINAL / GPU-Accelerated Construction of the Gabriel Graph: Parallelization Strategies and Applications to Large-Margin Classification and Graph-Based Clustering
Proposes CUDA parallelization strategies—implicit vertex-pair mapping, bitmask-based atomically compacted edge lists, and thread coarsening—reducing Gabriel graph construction time by two to nearly four orders of magnitude versus a sequential CPU baseline, without loss of classification accuracy on 14 public benchmarks, and enabling a clustering method that requires no explicit density radius.
01 ABSTRACT
Fact: The paper introduces three CUDA strategies—linear thread-index implicit mapping to vertex pairs, two-pass bitmask atomic edge-list compaction, and thread coarsening—to accelerate Gabriel graph construction. Fact: On 14 public benchmarks, the GPU implementation achieves up to 8484x speedup over a sequential CPU baseline with no loss of classification accuracy; the proposed clustering method is statistically competitive with DBSCAN on the Dunn index while eliminating the density radius parameter. Author view: These strategies make Gabriel graphs practical at larger scales and extend them to density-aware clustering.
02 KEY FINDINGS
- An implicit closed-form mapping assigns each linear thread index directly to a vertex pair (i,j), removing the O(N²) adjacency structure and enabling constant-time, constant-memory pair location.
- A two-pass, bitmask-based, atomically compacted edge-list construction produces a dense edge array proportional only to the number of edges actually found.
- Thread coarsening lets each thread evaluate several candidate pairs, trading launch and scheduling overhead against load balance.
AI GENERATED SUMMARY / DISCOVERED BY ARXIV CS.LG