Memory-Aware Framework for Efficient Second-Order Random Walk on Large Graphs

Second-order random walk is an important technique for graph analysis. Many applications use it to capture higher-order patterns in the graph, thus improving the model accuracy. However, the memory explosion problem of this technique hinders it from analyzing large graphs. When processing a billion-edge graph like Twitter, existing solutions (e.g., alias method) of the second-order random walk may take up 1796TB memory. Such high memory overhead comes from the memory-unaware strategies for node sampling across the graph. In this paper, to clearly study the efficiency of various node sampling methods in the context of second-order random walk, we design a cost model, and then propose a new node sampling method following the acceptance-rejection paradigm to achieve a better balance between memory and time cost. Further, to guarantee the efficiency of the second-order random walk within arbitrary memory budgets, we propose a memory-aware framework on the basis of the cost model. The framework applies a cost-based optimizer to assign desirable node sampling method for each node in the graph within a memory budget while minimizing the time cost. Finally, we provide general programming interfaces for users to benefit from the memory-aware framework easily. The empirical studies demonstrate that our memory-aware framework is robust with respect to memory and is able to achieve considerable efficiency by reducing 90% of the memory cost.