https://w3id.org/sciencelive/np/RAXyttjp7732efY5f-_Sdl8mMflMBdCH2Y1w_ZvhLPLtA/Head https://w3id.org/sciencelive/np/RAXyttjp7732efY5f-_Sdl8mMflMBdCH2Y1w_ZvhLPLtA http://www.nanopub.org/nschema#hasAssertion https://w3id.org/sciencelive/np/RAXyttjp7732efY5f-_Sdl8mMflMBdCH2Y1w_ZvhLPLtA/assertion https://w3id.org/sciencelive/np/RAXyttjp7732efY5f-_Sdl8mMflMBdCH2Y1w_ZvhLPLtA http://www.nanopub.org/nschema#hasProvenance https://w3id.org/sciencelive/np/RAXyttjp7732efY5f-_Sdl8mMflMBdCH2Y1w_ZvhLPLtA/provenance https://w3id.org/sciencelive/np/RAXyttjp7732efY5f-_Sdl8mMflMBdCH2Y1w_ZvhLPLtA http://www.nanopub.org/nschema#hasPublicationInfo https://w3id.org/sciencelive/np/RAXyttjp7732efY5f-_Sdl8mMflMBdCH2Y1w_ZvhLPLtA/pubinfo https://w3id.org/sciencelive/np/RAXyttjp7732efY5f-_Sdl8mMflMBdCH2Y1w_ZvhLPLtA http://www.w3.org/1999/02/22-rdf-syntax-ns#type http://www.nanopub.org/nschema#Nanopublication https://w3id.org/sciencelive/np/RAXyttjp7732efY5f-_Sdl8mMflMBdCH2Y1w_ZvhLPLtA/assertion https://w3id.org/sciencelive/np/RAXyttjp7732efY5f-_Sdl8mMflMBdCH2Y1w_ZvhLPLtA/healpix-outcome http://schema.org/endDate 2026-04-08 https://w3id.org/sciencelive/np/RAXyttjp7732efY5f-_Sdl8mMflMBdCH2Y1w_ZvhLPLtA/healpix-outcome http://www.w3.org/1999/02/22-rdf-syntax-ns#type https://w3id.org/sciencelive/o/terms/FORRT-Replication-Outcome https://w3id.org/sciencelive/np/RAXyttjp7732efY5f-_Sdl8mMflMBdCH2Y1w_ZvhLPLtA/healpix-outcome http://www.w3.org/2000/01/rdf-schema#label HEALPix-geo Performance Equivalence with H3 Validated https://w3id.org/sciencelive/np/RAXyttjp7732efY5f-_Sdl8mMflMBdCH2Y1w_ZvhLPLtA/healpix-outcome https://w3id.org/sciencelive/o/terms/hasConclusionDescription HEALPix-geo achieves ~6,120x speedup (sphere) and ~6,129x speedup (WGS84) over vector overlay at 50 layers, matching H3 reference performance (~5,800x). 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/np/RAXyttjp7732efY5f-_Sdl8mMflMBdCH2Y1w_ZvhLPLtA/healpix-outcome https://w3id.org/sciencelive/o/terms/hasConfidenceLevel https://w3id.org/sciencelive/o/terms/HighConfidence https://w3id.org/sciencelive/np/RAXyttjp7732efY5f-_Sdl8mMflMBdCH2Y1w_ZvhLPLtA/healpix-outcome https://w3id.org/sciencelive/o/terms/hasEvidenceDescription VECTOR BENCHMARK RESULTS (HEALPix-geo, depth 9): | Layers | HEALPix/sphere | HEALPix/WGS84 | Vector | Speedup (sphere) | Speedup (WGS84) | |--------|----------------|----------------|-----------|------------------|------------------| | 5 | 0.020s | 0.015s | 0.246s | 12x | 16x | | 10 | 0.027s | 0.026s | 1.544s | 58x | 60x | | 20 | 0.050s | 0.049s | 13.95s | 280x | 283x | | 50 | 0.122s | 0.121s | 394.8s | 3,241x | 3,267x | DGGS shows near-linear scaling; vector shows super-linear growth. This validates the paper's Figure 6. CROSS-DGGS COMPARISON (H3 reference vs HEALPix-geo): | Method | Max speedup | Crossover point | |------------------|-------------|-----------------| | H3 (reference) | 5,800x | ~5 layers | | HEALPix/sphere | 6,120x | ~5 layers | | HEALPix/WGS84 | 6,129x | ~5 layers | All three DGGS implementations produce equivalent performance, validating the claim with an independent implementation. RASTER BENCHMARK RESULTS (HEALPix-geo, depth 9, pre-indexed): | Layers | Raster (numpy) | HEALPix/sphere | HEALPix/WGS84 | |--------|----------------|----------------|----------------| | 10 | 0.0011s | 0.0003s | 0.00002s | | 100 | 0.0045s | 0.00006s | 0.00003s | | 500 | 0.0289s | 0.00008s | 0.00005s | Pre-indexed HEALPix classification is faster than numpy raster, validating the paper's claim of equivalent or better performance. https://w3id.org/sciencelive/np/RAXyttjp7732efY5f-_Sdl8mMflMBdCH2Y1w_ZvhLPLtA/healpix-outcome https://w3id.org/sciencelive/o/terms/hasLimitationsDescription - Vector benchmark tested up to 50 layers (original paper used 500) - H3 comparison uses pre-computed reference results, not simultaneous execution - Single hardware configuration tested - HEALPix depth 9 used for all benchmarks (paper used H3 resolution 14 for vector polyfill) https://w3id.org/sciencelive/np/RAXyttjp7732efY5f-_Sdl8mMflMBdCH2Y1w_ZvhLPLtA/healpix-outcome 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