Comparison of PageRank algorithm using various datatypes.
This experiment (rank-float-vs-double) was for comparing the performance between finding pagerank using 32-bit floats (float), and finding pagerank using 64-bit floats (double). Both datatypes were attempted on different types of graphs, running each technique 5 times per graph to get a good time measure.
It seems using double datatype increases execution time by 0-33%, when compared to float. With respect to GM-RATIO, using 64-bit floating point rank vector is 12% slower (0.89x) than using 32-bit floating point rank vector. With respect to AM-RATIO, using 64-bit floating point rank vector is 17% slower (0.85x). This could be attributed to increased memory bandwidth requirement. However, this overhead is somewhat large, despite the fact that most of the data for a graph is actually associated with the CSR representation, and not the rank vector. As the rank vector is accessed randomly, a high cache miss ratio might be the culprit here. Note that neither approach makes use of SIMD instructions which are available on all modern hardware.
This experiment (rank-float-vs-bfloat16) was for comparing the result between finding pagerank using float as the storage type, and finding pagerank using bfloat16 as the storage type. Both datatypes were attempted on different types of graphs, running each technique 5 times per graph to get a good time measure.
Unfortunately it seems bfloat16 cannot be used for PageRank as its too inaccurate (atleast when simply replacing float vectors with bfloat16 vectors). Using fp16 might work, but likely give negligible performance improvement over float. Note that neither approach makes use of SIMD instructions which are available on all modern hardware.
This experiment (cuda-rank-float-vs-double) was for comparing the performance between finding pagerank using 32-bit floats (float), and finding pagerank using 64-bit floats (double). Both datatypes were attempted on different types of graphs, running each technique 5 times per graph to get a good time measure.
It seems using double datatype increases execution time by 1-60%, when compared to float. With respect to GM-RATIO, using 64-bit floating point rank vector is 24% slower (0.81x) than using 32-bit floating point rank vector. With respect to AM-RATIO, using 64-bit floating point rank vector is 34% slower (0.75x). This could be attributed to increased memory bandwidth requirement. However, this overhead is somewhat large, despite the fact that most of the data for a graph is actually associated with the CSR representation, and not the rank vector. As the rank vector is accessed randomly, low memory coalescing might be the culprit here.
This experiment (nvgraph-rank-float-vs-double) was for comparing the performance between finding pagerank using 32-bit floats (float), and finding pagerank using 64-bit floats (double). Both datatypes were attempted on different types of graphs, running each technique 5 times per graph to get a good time measure.
It seems using double datatype increases execution time by 17-103%, when compared to float. With respect to GM-RATIO, using 64-bit floating point rank vector is 52% slower (0.66x) than using 32-bit floating point rank vector. With respect to AM-RATIO, using 64-bit floating point rank vector is 67% slower (0.60x). This could be attributed to increased memory bandwidth requirement. However, this overhead is significant, despite the fact that most of the data for a graph is actually associated with the CSR representation, and not the rank vector. As the rank vector is quite likely accessed randomly, low memory coalescing might be the culprit here.
This experiment (csr-int32-vs-int64) was for comparing the performance between finding pagerank using 32-bit ints (int32), and finding pagerank using 64-bit ints (int64). Both datatypes were attempted on different types of graphs, running each technique 5 times per graph to get a good time measure.
It seems using int64 datatype increases execution time by 1-16%, when compared to int32. With respect to GM-RATIO as well as AM-RATIO, using 64-bit integer CSR representation is 9% slower (0.92x) than using 32-bit integer CSR representation. This could be attributed to increased memory bandwidth requirement. However, this overhead is quite small, despite the fact that most of the data for a graph is actually associated with the CSR representation. As the CSR representation is accessed linearly, improved cache usage might be the saviour here. Note that neither approach makes use of SIMD instructions which are available on all modern hardware.
This experiment (cuda-csr-int32-vs-int64) was for comparing the performance between find pagerank using 32-bit ints (int32), and finding pagerank using 64-bit ints (int64). Both datatypes were attempted on different types of graphs, running each technique 5 times per graph to get a good time measure.
It seems using int64 datatype increases execution time by 6-35%, when compared to int32. With respect to GM-RATIO, using 64-bit integer CSR representation is 17% slower (0.85x) than using 32-bit integer CSR representation. With respect to AM-RATIO, using 64-bit integer CSR representation is 24% slower (0.81x). This could be attributed to increased memory bandwidth requirement. However, this overhead is somewhat small, despite the fact that most of the data for a graph is actually associated with the CSR representation. As the CSR representation is accessed linearly, improved memory coalescing might be the saviour here.
- CUDA by Example :: Jason Sanders, Edward Kandrot
- Adjusting PageRank parameters and Comparing results
- PageRank Algorithm, Mining massive Datasets (CS246), Stanford University
- SuiteSparse Matrix Collection
