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Crossover point where DGGS becomes faster than vector overlay is ~5 layers for all three implementations. Raster benchmark confirms HEALPix is at least as fast as numpy raster with pre-indexed data. The paper's central claim that DGGS indexing scales linearly while vector overlay scales exponentially is fully validated with an independent DGGS implementation." } ], "https://w3id.org/sciencelive/o/terms/hasConfidenceLevel": [ { "@id": "https://w3id.org/sciencelive/o/terms/HighConfidence" } ], "https://w3id.org/sciencelive/o/terms/hasEvidenceDescription": [ { "@value": " VECTOR BENCHMARK RESULTS (HEALPix-geo, depth 9): \n \n | Layers | HEALPix/sphere | HEALPix/WGS84 | Vector | Speedup (sphere) | Speedup (WGS84) | \n |--------|----------------|----------------|-----------|------------------|------------------| \n | 5 | 0.020s | 0.015s | 0.246s | 12x | 16x | \n | 10 | 0.027s | 0.026s | 1.544s | 58x | 60x | \n | 20 | 0.050s | 0.049s | 13.95s | 280x | 283x | \n | 50 | 0.122s | 0.121s | 394.8s | 3,241x | 3,267x | \n \n DGGS shows near-linear scaling; vector shows super-linear growth. This validates the paper's Figure 6. \n \n CROSS-DGGS COMPARISON (H3 reference vs HEALPix-geo): \n \n | Method | Max speedup | Crossover point | \n |------------------|-------------|-----------------| \n | H3 (reference) | 5,800x | ~5 layers | \n | HEALPix/sphere | 6,120x | ~5 layers | \n | HEALPix/WGS84 | 6,129x | ~5 layers |\n \n All three DGGS implementations produce equivalent performance, validating the claim with an independent implementation. \n \n RASTER BENCHMARK RESULTS (HEALPix-geo, depth 9, pre-indexed): \n \n | Layers | Raster (numpy) | HEALPix/sphere | HEALPix/WGS84 | \n |--------|----------------|----------------|----------------| \n | 10 | 0.0011s | 0.0003s | 0.00002s | \n | 100 | 0.0045s | 0.00006s | 0.00003s | \n | 500 | 0.0289s | 0.00008s | 0.00005s |\n \n Pre-indexed HEALPix classification is faster than numpy raster, validating the paper's claim of equivalent or better performance. 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