in the same spirit of the above comment, the webcola core seems to be doing O(n^2) comparisons. probably somewhere in the top 10 for cool foundational scientific computing algorithms that people like here are barnes hut, which cuts the comparisons to O(n log n), and fancier, fast multipole. basically, no need to precisely compare far apart things, which are most of them. by the time of something like interactive UIs over 100K+ nodes, the asymptotics costs start dominating everything, and 2-8X C/SIMD speedups get overwhelmed if you don't scale the core alg. this is at the heart of many modern ML algorithms as well: many need to iteratively compare vectors, such as knn and umap.
pretty neat as well is that barnes hut + multipole are also SIMD friendly, and even better, GPU friendly. it is a bit trickier b/c now dealing with ideas like SIMD/GPU tree construction, but still works! for graphistry, our engine prototype had a multicore wasm frontend impl, gpu webcl frontend impl, and gpu opencl backend impl, and just by adding that, got some pretty cool #'s. nowdays we do a bit wilder and focus more on other layers like interactive analytics, bigger-than-memory, connectors/collaboration/embedding/etc, but all are logical steps building on what is being described here. bravo!
edit: it's good the blogpost included rendering. rendering gets pretty fun with graphs b/c while points are ~easy, edges get at (a) dynamic geometry (b) that can span the screen and (c) blow up in count pretty quick. ouch! the pathfinder project for vector text rendering is a fun related effort for what it takes to speed that up with simd/gpu. if someone is interested in a webgl contract around helping our users explore bigger interactive graphs (webgl/react client <-apache arrow-> python/CUDA server), ping [email protected] !
in the same spirit of the above comment, the webcola core seems to be doing O(n^2) comparisons. probably somewhere in the top 10 for cool foundational scientific computing algorithms that people like here are barnes hut, which cuts the comparisons to O(n log n), and fancier, fast multipole. basically, no need to precisely compare far apart things, which are most of them. by the time of something like interactive UIs over 100K+ nodes, the asymptotics costs start dominating everything, and 2-8X C/SIMD speedups get overwhelmed if you don't scale the core alg. this is at the heart of many modern ML algorithms as well: many need to iteratively compare vectors, such as knn and umap.
pretty neat as well is that barnes hut + multipole are also SIMD friendly, and even better, GPU friendly. it is a bit trickier b/c now dealing with ideas like SIMD/GPU tree construction, but still works! for graphistry, our engine prototype had a multicore wasm frontend impl, gpu webcl frontend impl, and gpu opencl backend impl, and just by adding that, got some pretty cool #'s. nowdays we do a bit wilder and focus more on other layers like interactive analytics, bigger-than-memory, connectors/collaboration/embedding/etc, but all are logical steps building on what is being described here. bravo!
edit: it's good the blogpost included rendering. rendering gets pretty fun with graphs b/c while points are ~easy, edges get at (a) dynamic geometry (b) that can span the screen and (c) blow up in count pretty quick. ouch! the pathfinder project for vector text rendering is a fun related effort for what it takes to speed that up with simd/gpu. if someone is interested in a webgl contract around helping our users explore bigger interactive graphs (webgl/react client <-apache arrow-> python/CUDA server), ping [email protected] !