Theoretically Efficient Parallel Graph Algorithms Can Be Fast and Scalable

There has been significant recent interest in parallel graph processing due to the need to quickly analyze the large graphs available today. Many graph codes have been designed for distributed memory or external memory. However, today even the largest publicly-available real-world graph (the Hyperlink Web graph with over 3.5 billion vertices and 128 billion edges) can fit in the memory of a single commodity multicore server. Nevertheless, most experimental work in the literature report results on much smaller graphs, and the ones for the Hyperlink graph use distributed or external memory. Therefore, it is natural to ask whether we can efficiently solve a broad class of graph problems on this graph in memory. This paper shows that theoretically-efficient parallel graph algorithms can scale to the largest publicly-available graphs using a single machine with a terabyte of RAM, processing them in minutes. We give implementations of theoretically-efficient parallel algorithms for 20 important graph problems. We also present the optimizations and techniques that we used in our implementations, which were crucial in enabling us to process these large graphs quickly. We show that the running times of our implementations outperform existing state-of-the-art implementations on the largest real-world graphs. For many of the problems that we consider, this is the first time they have been solved on graphs at this scale. We have made the implementations developed in this work publicly-available as the Graph-Based Benchmark Suite (GBBS).Comment: This is the full version of the paper appearing in the ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), 201

Verification and Synthesis of Symmetric Uni-Rings for Leads-To Properties

This paper investigates the verification and synthesis of parameterized protocols that satisfy leadsto properties $R \leadsto Q$ on symmetric unidirectional rings (a.k.a. uni-rings) of deterministic and constant-space processes under no fairness and interleaving semantics, where $R$ and $Q$ are global state predicates. First, we show that verifying $R \leadsto Q$ for parameterized protocols on symmetric uni-rings is undecidable, even for deterministic and constant-space processes, and conjunctive state predicates. Then, we show that surprisingly synthesizing symmetric uni-ring protocols that satisfy $R \leadsto Q$ is actually decidable. We identify necessary and sufficient conditions for the decidability of synthesis based on which we devise a sound and complete polynomial-time algorithm that takes the predicates $R$ and $Q$, and automatically generates a parameterized protocol that satisfies $R \leadsto Q$ for unbounded (but finite) ring sizes. Moreover, we present some decidability results for cases where leadsto is required from multiple distinct $R$ predicates to different $Q$ predicates. To demonstrate the practicality of our synthesis method, we synthesize some parameterized protocols, including agreement and parity protocols

Parallel Maximum Clique Algorithms with Applications to Network Analysis and Storage

We propose a fast, parallel maximum clique algorithm for large sparse graphs that is designed to exploit characteristics of social and information networks. The method exhibits a roughly linear runtime scaling over real-world networks ranging from 1000 to 100 million nodes. In a test on a social network with 1.8 billion edges, the algorithm finds the largest clique in about 20 minutes. Our method employs a branch and bound strategy with novel and aggressive pruning techniques. For instance, we use the core number of a vertex in combination with a good heuristic clique finder to efficiently remove the vast majority of the search space. In addition, we parallelize the exploration of the search tree. During the search, processes immediately communicate changes to upper and lower bounds on the size of maximum clique, which occasionally results in a super-linear speedup because vertices with large search spaces can be pruned by other processes. We apply the algorithm to two problems: to compute temporal strong components and to compress graphs.Comment: 11 page

Gunrock: GPU Graph Analytics

For large-scale graph analytics on the GPU, the irregularity of data access and control flow, and the complexity of programming GPUs, have presented two significant challenges to developing a programmable high-performance graph library. "Gunrock", our graph-processing system designed specifically for the GPU, uses a high-level, bulk-synchronous, data-centric abstraction focused on operations on a vertex or edge frontier. Gunrock achieves a balance between performance and expressiveness by coupling high performance GPU computing primitives and optimization strategies with a high-level programming model that allows programmers to quickly develop new graph primitives with small code size and minimal GPU programming knowledge. We characterize the performance of various optimization strategies and evaluate Gunrock's overall performance on different GPU architectures on a wide range of graph primitives that span from traversal-based algorithms and ranking algorithms, to triangle counting and bipartite-graph-based algorithms. The results show that on a single GPU, Gunrock has on average at least an order of magnitude speedup over Boost and PowerGraph, comparable performance to the fastest GPU hardwired primitives and CPU shared-memory graph libraries such as Ligra and Galois, and better performance than any other GPU high-level graph library.Comment: 52 pages, invited paper to ACM Transactions on Parallel Computing (TOPC), an extended version of PPoPP'16 paper "Gunrock: A High-Performance Graph Processing Library on the GPU