A great number of graph analysis algorithms involve iterative computations, which dominate the runtime. Accelerating iterative graph computations has become the key to improving the performance of graph algorithms. While numerous studies have focused on reducing the runtime of each iteration to improve efficiency, the optimization of the number of iterations is often overlooked. In this work, we first establish a correlation between vertex processing order and the number of iterations, providing an opportunity to reduce the number of iterations. We propose a metric function to evaluate the effectiveness of vertex processing order in accelerating iterative computations. Leveraging this metric, we propose a novel graph reordering method, GoGraph, which constructs an efficient vertex processing order. Additionally, for evolving graphs, we further propose a metric function designed to evaluate the effectiveness of vertex processing orders in response to graph changes and provide three optional methods for dynamically adjusting the vertex processing order. Our experimental results illustrate that GoGraph sur passes current state-of-the-art reordering algorithms, improving runtime by an average of 1.83× (up to 3.34×). Compared to traditional synchronous computation methods, our approach enhances the speed of iterative computations by up to 6.30×. In dynamic scenarios, incremental GoGraph can reduce end-to-end time by 43% on average (up to 48%).

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 compu-tation. 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 1.83 x on average (up to 3.34 x) in runtime. Compared with traditional synchronous computation, our method improves the iterative computations up to 6.30 x in runtime.