  The emerging Graph Convolutional Network (GCN) has now been widely used in
many domains, and it is challenging to improve the efficiencies of applications
by accelerating the GCN trainings. For the sparsity nature and exploding scales
of input real-world graphs, state-of-the-art GCN training systems (e.g.,
GNNAdvisor) employ graph processing techniques to accelerate the message
exchanging (i.e. aggregations) among the graph vertices. Nevertheless, these
systems treat both the aggregation stages of forward and backward propagation
phases as all-active graph processing procedures that indiscriminately conduct
computation on all vertices of an input graph.
  In this paper, we first point out that in a GCN training problem with a given
training set, the aggregation stages of its backward propagation phase (called
as backward aggregations in this paper) can be converted to partially-active
graph processing procedures, which conduct computation on only partial vertices
of the input graph. By leveraging such a finding, we propose an execution path
preparing method that collects and coalesces the data used during backward
propagations of GCN training conducted on GPUs. The experimental results show
that compared with GNNAdvisor, our approach improves the performance of the
backward aggregation of GCN trainings on typical real-world graphs by
1.48x~5.65x. Moreover, the execution path preparing can be conducted either
before the training (during preprocessing) or on-the-fly with the training.
When used during preprocessing, our approach improves the overall GCN training
by 1.05x~1.37x. And when used on-the-fly, our approach improves the overall GCN
training by 1.03x~1.35x.
