  Enhancing the efficiency of iterative computation on graphs has garnered
considerable attention in both industry and academia. Nonetheless, the majority
of efforts focus on expediting iterative computation by minimizing the running
time per iteration step, ignoring the optimization of the number of iteration
rounds, which is a crucial aspect of iterative computation. We experimentally
verified the correlation between the vertex processing order and the number of
iterative rounds, thus making it possible to reduce the number of execution
rounds for iterative computation. In this paper, we propose a graph reordering
method, GoGraph, which can construct a well-formed vertex processing order
effectively reducing the number of iteration rounds and, consequently,
accelerating iterative computation. Before delving into GoGraph, a metric
function is introduced to quantify the efficiency of vertex processing order in
accelerating iterative computation. This metric reflects the quality of the
processing order by counting the number of edges whose source precedes the
destination. GoGraph employs a divide-and-conquer mindset to establish the
vertex processing order by maximizing the value of the metric function. Our
experimental results show that GoGraph outperforms current state-of-the-art
reordering algorithms by 1.83x on average (up to 3.34x) in runtime.
