Duane Merrill (NVIDIA) - GPU Technology Conference

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Quadratic-work approach• Input: Vertex set V, row-offsets array R, column-indices array C,source vertex s• Output: Array dist[0..n-1] with dist[v] holding the distance from sto vkernel kernel1. parallel for (i in V) :2. dist[i] := ∞3. dist[s] := 04. iteration := 05. do :6. done := true7. parallel for (i in V) :8. if (dist[i] == iteration)9. done := false10. for (offset in R[i] .. R[i+1]-1) :11. j := C[offset]12. dist[j] = iteration + 113. iteration++14. while (!done)Good: trivial data-parallel <strong>GPU</strong> stencilsBad: worst-case quadratic O(n 2 +m) workHarish et al., Deng et al. Hong et al20
Vertices (millions)Vertices (millions)Vertices (millions)Vertices (millions)Vertices (millions)Vertices (millions)Active edges per iteration300.51402520151050.40.30.20.11201008060402000 2 4 6 8 10 12 14 16 18Search Depth0.00 100 200 300 400 500 600 700 800Search Depth00 1 2 3 4Search DepthWikipedia 3D cubic lattice R-MAT small-world0.030550.025440.0200.0150.01032320.005110.0000 3000 6000 9000 12000 15000Search Depth00 20 40 60 80 100 120 140 160Search Depth00 4 8 12 16 20 24 28 32 36 40 44 48 52Search DepthEurope road atlasPDE-constrainedoptimizationAuto transmission mesh21
Page 1 and 2: Duane Merrill (NVIDIA)Michael Garla
Page 4 and 5: Sparse graphsGraph G(V, E) where n
Page 6: Compressed sparse row (CSR) represe
Page 9 and 10: Breadth-first search (BFS)1. Pick a
Page 11 and 12: Breadth-first search (BFS)1. Pick a
Page 13 and 14: BFS applicationsAlgorithmic primiti
Page 15 and 16: Common parallelization strategies
Page 17 and 18: Quadratic-work approach1. Inspect e
Page 19: Quadratic-work approach1. Inspect e
Page 23 and 24: Referenced vertex identifiers(milli
Page 25 and 26: Linear-work challenges for parallel
Page 27 and 28: Prefix sum for allocationAllocation
Page 29 and 30: Data-flow of efficient CTA scan(gra
Page 31 and 32: 2) Poor load balancing within SIMD
Page 33 and 34: 4) SIMD simultaneous discovery0 1 2
Page 35 and 36: Single-socket comparisonGraphSpy Pl
Page 38 and 39: Maximal independent setA vertex sub
Page 40 and 41: MIS applicationsGraph coloring (ver
Page 42 and 43: The sequential algorithm• Repeate
Page 44 and 45: Data-parallel GPU approach• Input
Page 46 and 47: SummaryPurely data-parallel approac
Page 48 and 49: GTC 2013:The Premier Event in Accel
Page 50 and 51: Comparison of expansion techniques5
Page 52 and 53: 10 9 edges / secnormalizedCompariso
Page 54: 10 9 edges / secnormalizedMulti-GPU

Duane Merrill (NVIDIA) - GPU Technology Conference

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