Julienne: A Framework for Parallel Graph Algorithms using Work-efficient Bucketing

Existing graph-processing frameworks let users develop efficient implementations for many graph problems, but none of them support efficiently bucketing vertices, which is needed for bucketing-based graph algorithms such as \Delta-stepping and approximate set-cover. Motivated by the lack of simple, scalable, and efficient implementations of bucketing-based algorithms, we develop the Julienne framework, which extends a recent shared-memory graph processing framework called Ligra with an interface for maintaining a collection of buckets under vertex insertions and bucket deletions. We provide a theoretically efficient parallel implementation of our bucketing interface and study several bucketing-based algorithms that make use of it (either bucketing by remaining degree or by distance) to improve performance: the peeling algorithm for k-core (coreness), \Delta-stepping, weighted breadth-first search, and approximate set cover. The implementations are all simple and concise (under 100 lines of code). Using our interface, we develop the first work-efficient parallel algorithm for k-core in the literature with nontrivial parallelism. We experimentally show that our bucketing implementation scales well and achieves high throughput on both synthetic and real-world workloads. Furthermore, the bucketing-based algorithms written in Julienne achieve up to 43x speedup on 72 cores with hyper-threading over well-tuned sequential baselines, significantly outperform existing work-inefficient implementations in Ligra, and either outperform or are competitive with existing special-purpose parallel codes for the same problem. We experimentally study our implementations on the largest publicly available graphs and show that they scale well in practice, processing real-world graphs with billions of edges in seconds, and hundreds of billions of edges in a few minutes. As far as we know, this is the first time that graphs at this scale have been analyzed in the main memory of a single multicore machine.