  In this paper, we aim at improving the computational efficiency of graph
convolutional networks (GCNs) for learning on point clouds. The basic graph
convolution that is typically composed of a $K$-nearest neighbor (KNN) search
and a multilayer perceptron (MLP) is examined. By mathematically analyzing the
operations there, two findings to improve the efficiency of GCNs are obtained.
(1) The local geometric structure information of 3D representations propagates
smoothly across the GCN that relies on KNN search to gather neighborhood
features. This motivates the simplification of multiple KNN searches in GCNs.
(2) Shuffling the order of graph feature gathering and an MLP leads to
equivalent or similar composite operations. Based on those findings, we
optimize the computational procedure in GCNs. A series of experiments show that
the optimized networks have reduced computational complexity, decreased memory
consumption, and accelerated inference speed while maintaining comparable
accuracy for learning on point clouds. Code will be available at
\url{https://github.com/ofsoundof/EfficientGCN.git}.
