What is Twitter

The Art of Multiprocessor Programming

In this paper, we present GridGraph, a system for processing large-scale graphs on a single machine. Grid-Graph breaks graphs into 1D-partitioned vertex chunks and 2D-partitioned edge blocks using a first fine-grained level partitioning in preprocessing. A second coarse-grained level partitioning is applied in runtime. Through a novel dual sliding windows method, GridGraph can stream the edges and apply on-the-fly vertex updates, thus reduce the I/O amount required for computation. The partitioning of edges also enable selective scheduling so that some of the blocks can be skipped to reduce unnecessary I/O. This is very effective when the active vertex set shrinks with convergence.

Our evaluation results show that GridGraph scales seamlessly with memory capacity and disk bandwidth, and outperforms state-of-the-art out-of-core systems, including GraphChi and X-Stream. Furthermore, we show that the performance of GridGraph is even competitive with distributed systems, and it also provides significant cost efficiency in cloud environment.

/pdf/gridgraph-large-scale-graph-processing-on-a-single-machine-2t1iqmbo27.pdf

GridGraph: large-scale graph processing on a single machine using 2-level hierarchical partitioning

The vertex-centric programming model is an established computational paradigm recently incorporated into distributed processing frameworks to address challenges in large-scale graph processing. Billion-node graphs that exceed the memory capacity of commodity machines are not well supported by popular Big Data tools like MapReduce, which are notoriously poor performing for iterative graph algorithms such as PageRank. In response, a new type of framework challenges one to “think like a vertex” (TLAV) and implements user-defined programs from the perspective of a vertex rather than a graph. Such an approach improves locality, demonstrates linear scalability, and provides a natural way to express and compute many iterative graph algorithms. These frameworks are simple to program and widely applicable but, like an operating system, are composed of several intricate, interdependent components, of which a thorough understanding is necessary in order to elicit top performance at scale. To this end, the first comprehensive survey of TLAV frameworks is presented. In this survey, the vertex-centric approach to graph processing is overviewed, TLAV frameworks are deconstructed into four main components and respectively analyzed, and TLAV implementations are reviewed and categorized.

https://dl.acm.org/doi/pdf/10.1145/2818185

Thinking Like a Vertex: A Survey of Vertex-Centric Frameworks for Large-Scale Distributed Graph Processing

Natural graphs with skewed distributions raise unique challenges to distributed graph computation and partitioning. Existing graph-parallel systems usually use a “one-size-fits-all” design that uniformly processes all vertices, which either suffer from notable load imbalance and high contention for high-degree vertices (e.g., Pregel and GraphLab) or incur high communication cost and memory consumption even for low-degree vertices (e.g., PowerGraph and GraphX). In this article, we argue that skewed distributions in natural graphs also necessitate differentiated processing on high-degree and low-degree vertices. We then introduce PowerLyra, a new distributed graph processing system that embraces the best of both worlds of existing graph-parallel systems. Specifically, PowerLyra uses centralized computation for low-degree vertices to avoid frequent communications and distributes the computation for high-degree vertices to balance workloads. PowerLyra further provides an efficient hybrid graph partitioning algorithm (i.e., hybrid-cut) that combines edge-cut (for low-degree vertices) and vertex-cut (for high-degree vertices) with heuristics. To improve cache locality of inter-node graph accesses, PowerLyra further provides a locality-conscious data layout optimization. PowerLyra is implemented based on the latest GraphLab and can seamlessly support various graph algorithms running in both synchronous and asynchronous execution modes. A detailed evaluation on three clusters using various graph-analytics and MLDM (Machine Learning and Data Mining) applications shows that PowerLyra outperforms PowerGraph by up to 5.53X (from 1.24X) and 3.26X (from 1.49X) for real-world and synthetic graphs, respectively, and is much faster than other systems like GraphX and Giraph, yet with much less memory consumption. A porting of hybrid-cut to GraphX further confirms the efficiency and generality of PowerLyra.

PowerLyra: Differentiated Graph Computation and Partitioning on Skewed Graphs

We study compression techniques for parallel in-memory graph algorithms, and show that we can achieve reduced space usage while obtaining competitive or improved performance compared to running the algorithms on uncompressed graphs. We integrate the compression techniques into Ligra, a recent shared-memory graph processing system. This system, which we call Ligra+, is able to represent graphs using about half of the space for the uncompressed graphs on average. Furthermore, Ligra+ is slightly faster than Ligra on average on a 40-core machine with hyper-threading. Our experimental study shows that Ligra+ is able to process graphs using less memory, while performing as well as or faster than Ligra.

/pdf/smaller-and-faster-parallel-processing-of-compressed-graphs-3xmhdda4dz.pdf

Smaller and Faster: Parallel Processing of Compressed Graphs with Ligra+

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.

https://dl.acm.org/doi/pdf/10.1145/3087556.3087580

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

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 13 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 provide a publicly-available benchmark suite containing our implementations.

https://dl.acm.org/doi/pdf/10.1145/3210377.3210414

Theoretically Efficient Parallel Graph Algorithms Can Be Fast and Scalable

Graph reordering is a powerful technique to increase the locality of the representations of graphs, which can be helpful in several applications. We study how the technique can be used to improve compression of graphs and inverted indexes. We extend the recent theoretical model of Chierichetti et al. (KDD 2009) for graph compression, and show how it can be employed for compression-friendly reordering of social networks and web graphs and for assigning document identifiers in inverted indexes. We design and implement a novel theoretically sound reordering algorithm that is based on recursive graph bisection. Our experiments show a significant improvement of the compression rate of graph and indexes over existing heuristics. The new method is relatively simple and allows efficient parallel and distributed implementations, which is demonstrated on graphs with billions of vertices and hundreds of billions of edges.

https://dl.acm.org/doi/pdf/10.1145/2939672.2939862

Compressing Graphs and Indexes with Recursive Graph Bisection

There has been a growing interest in the graph-streaming setting where a continuous stream of graph updates is mixed with graph queries. In principle, purely-functional trees are an ideal fit for this setting as they enable safe parallelism, lightweight snapshots, and strict serializability for queries. However, directly using them for graph processing leads to significant space overhead and poor cache locality. This paper presents C-trees, a compressed purely-functional search tree data structure that significantly improves on the space usage and locality of purely-functional trees. We design theoretically-efficient and practical algorithms for performing batch updates to C-trees, and also show that we can store massive dynamic real-world graphs using only a few bytes per edge, thereby achieving space usage close to that of the best static graph processing frameworks. To study the efficiency and applicability of our data structure, we designed Aspen, a graph-streaming framework that extends the interface of Ligra with operations for updating graphs. We show that Aspen is faster than two state-of-the-art graph-streaming systems, Stinger and LLAMA, while requiring less memory, and is competitive in performance with the state-of-the-art static graph frameworks, Galois, GAP, and Ligra+. With Aspen, we are able to efficiently process the largest publicly-available graph with over two hundred billion edges in the graph-streaming setting using a single commodity multicore server with 1TB of memory.

https://dl.acm.org/doi/pdf/10.1145/3314221.3314598

Laxman Dhulipala

Papers

Smaller and Faster: Parallel Processing of Compressed Graphs with Ligra+

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

Theoretically Efficient Parallel Graph Algorithms Can Be Fast and Scalable

Compressing Graphs and Indexes with Recursive Graph Bisection

Low-latency graph streaming using compressed purely-functional trees