Buffered Streaming Graph Partitioning

Abstract

Partitioning graphs into blocks of roughly equal size is a widely used tool when processing large graphs. Currently, there is a gap observed in the space of available partitioning algorithms. On the one hand, there are streaming algorithms that have been adopted to partition massive graph data on small machines. In the streaming model, vertices arrive one at a time including their neighborhood, and then have to be assigned directly to a block. These algorithms can partition huge graphs quickly with little memory, but they produce partitions with low solution quality. On the other hand, there are offline (shared-memory) multilevel algorithms that produce partitions with high-quality but also need a machine with enough memory to partition huge networks. In this work, we make a first step to close this gap by presenting an algorithm that computes significantly improved partitions of huge graphs using a single machine with little memory in a streaming setting. First, we adopt the buffered streaming model which is a more reasonable approach in practice. In this model, a processing element can store a buffer of nodes alongside with their edges before making assignment decisions. When our algorithm receives a batch of nodes, we build a model graph that represents the nodes of the batch and the already present partition structure. This model enables us to apply multilevel algorithms and in turn, on cheap machines, compute much higher quality solutions of huge graphs than previously possible. To partition the model graph, we develop a multilevel algorithm that optimizes an objective function that has previously been shown to be effective for the streaming setting. Surprisingly, this also removes the dependency on the number of blocks k from the running time compared to the previous state-of-the-art. Overall, our algorithm computes, on average, 75.9% better solutions than Fennel  [ 35 ] using a very small buffer size. In addition, for large values of k our algorithm becomes faster than Fennel .