R-MAT (for Recursive MATrix) is a simple, widely used model for generating graphs with a power law degree distribution, a small diameter, and communitys structure. It is particularly attractive for generating very large graphs because edges can be generated independently by an arbitrary number of processors. However, current R-MAT generators need time logarithmic in the number of nodes for generating an edge— constant time for generating one bit at a time for node IDs of the connected nodes. We achieve constant time per edge by precomputing pieces of node IDs of logarithmic length. Using an alias table data structure, these pieces can then be sampled in constant time. This simple technique leads to practical improvements by an order of magnitude. This further pushes the limits of attainable graph size and makes generation overhead negligible in most situations.

中文翻译：

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R-MAT 图的线性工作生成

R-MAT（用于递归矩阵）是一种简单、广泛使用的模型，用于生成具有幂律度分布、小直径和社区结构的图。它对于生成非常大的图特别有吸引力，因为边可以由任意数量的处理器独立生成。然而，当前的 R-MAT 生成器需要与节点数量成对数的时间来生成一条边——用于为连接节点的节点 ID 一次生成一位的恒定时间。我们通过预先计算对数长度的节点 ID 片段来实现每条边的恒定时间。使用别名表数据结构，然后可以在恒定时间内对这些片段进行采样。这种简单的技术导致了一个数量级的实际改进。这进一步推动了可达到的图大小的限制，并使生成开销在大多数情况下可以忽略不计。