  All-gather collective communication is one of the most important
communication primitives in parallel and distributed computation, which plays
an essential role in many HPC applications such as distributed Deep Learning
(DL) with model and hybrid parallelism. To solve the communication bottleneck
of All-gather, optical interconnection network can provide unprecedented high
bandwidth and reliability for data transfer among the distributed nodes.
However, most traditional All-gather algorithms are designed for electrical
interconnection, which cannot fit well for optical interconnect systems,
resulting in poor performance. This paper proposes an efficient scheme, called
OpTree, for All-gather operation on optical interconnect systems. OpTree
derives an optimal $m$-ary tree corresponding to the optimal number of
communication stages, achieving minimum communication time. We further analyze
and compare the communication steps of OpTree with existing All-gather
algorithms. Theoretical results exhibit that OpTree requires much less number
of communication steps than existing All-gather algorithms on optical
interconnect systems. Simulation results show that OpTree can reduce
communication time by 72.21%, 94.30%, and 88.58%, respectively, compared with
three existing All-gather schemes, WRHT, Ring, and NE.
