As a fundamental tool for graph analysis, random walk receives extensive attention in both industry and academia. For computing massive random walks, recent works show that GPUs provide a good option to accelerate the performance. However, due to the limited memory space of modern GPUs, it is infeasible to have both the graph data and walk index fully reside in GPU memory when running large-scale random walks. Thus, it necessitates an out-of-GPU-memory design, but this inevitably induces large amounts of CPU-GPU data transmission traffic and thus hinders the overall performance. In this paper, we develop LightTraffic, which optimizes the data transmission between CPU and GPU memory under the constraint of GPU memory capacity with various system designs, including a memory-efficient scheme for partition-based management and multiple scheduling techniques. LightTraffic is a fully out-of-GPU-memory design, so it supports running large-scale random walks on GPUs. Experiments on our prototype show that LightTraffic outperforms various state-of-the-art CPU-based in-memory systems which also support large-scale random walks. For example, compared to the CPU-based systems FlashMob and ThunderRW, which are highly optimized for random walks, LightTraffic achieves 1.7−5.0× and 1.4 − 12.8× performance speedup, respectively. It also achieves up to an order of magnitude speedup when compared to the GPU-based system Subway which also supports large-scale random walks with an out-of-GPU-memory design for graph data.

Random walk is widely applied to sample large-scale graphs due to its simplicity of implementation and solid theoretical foundations of bias analysis. However, its computational efficiency is heavily limited by theslow convergencerate (a.k.a. long burn-in period). To address this issue, we propose a common neighbor aware random walk framework called CNARW, which leverages weighted walking by differentiating the next-hop candidate nodes to speed up the convergence. Specifically, CNARW takes into consideration the common neighbors between previously visited nodes and next-hop candidate nodes in each walking step. Based on CNARW, we further develop two efficient “unbiased sampling” schemes, and we also design two variant algorithms which can reduce sampling cost and speed up the convergence. Experimental results on real-world network datasets show that our approach converges remarkably faster than the state-of-the-art random walk sampling algorithms; and to achieve the same estimation accuracy, our approach reduces the query cost significantly. Last, we use two case studies to demonstrate the effectiveness of our sampling framework in solving large-scale graph analysis tasks.

Random walk sampling is often used to conduct statistical estimation over graphs. This paper develops an algorithmic framework to reduce the mean square error of such statistical estimation. Our algorithmic framework is inspired by that the mean square error can be decomposed into a sum of the bias and variance of the estimator. More specifically, we apply the bootstrapping technique to design a bias reduction algorithm. Our bias reduction algorithm only utilizes a small number of valid sub-samples, which can reduce more bias of the estimator but may increase the variance of the estimator significantly. We use multiple parallel random walks to reduce this variance such that it can be reduced to arbitrarily small by deploying a sufficient number of random walks. We provide theoretical guarantees and computational complexity analysis of our proposed bias reduction algorithms. Also, the proposed bias reduction algorithm is generic and can be applied to optimize a large class of random walk sampling algorithms. Extensive experiments on four public datasets confirm the effectiveness and computational efficiency of our proposed algorithmic framework under the mean square metric and beyond.

Persistent key-value (KV) stores are mainly designed based on the Log-Structured Merge-tree (LSM-tree), yet they suffer from large read and write amplifications, especially when KV stores grow in size. Existing design optimizations for LSM-tree-based KV stores often make certain trade-offs and fail to simultaneously improve both the read and write performance on large KV stores without sacrificing scan performance. We design UniKV, which unifies the key design ideas of hash indexing and the LSM-tree in a single system. Specifically, UniKV leverages data locality to differentiate the indexing management of KV pairs. It also develops multiple techniques (e.g., merge with partial KV separation, dynamic range partitioning) to tackle the issues caused by unifying the indexing techniques, so as to simultaneously improve the performance in reads and writes. Furthermore, it proposes a parallel optimization scheme to manage partitions in parallel and develops multiple strategies to optimize the scan performance. Experiments show that UniKV significantly outperforms several state-of-the-art KV stores (e.g., LevelDB, RocksDB, PebblesDB and Titan) in overall throughput under read-write mixed workloads.

Graphs are commonly used in various applications such as online social networks (OSNs), E-commerce systems and social recommender systems. Random walk sampling is often used to conduct statistical estimation over such graphs. This paper develops an algorithmic framework to reduce the mean square error of such statistical estimation. Our algorithmic framework is inspired by that the mean square error can be decomposed into a sum of the bias and variance of the estimator. More specifically, we apply the bootstrapping technique to design a bias reduction algorithm. A new feature of this bias reduction algorithm is that it allows the variance to increase whenever the bias can be further reduced. The increased variance may lead to a large mean square error of the estimator. We use multiple parallel random walks to reduce this variance such that it can be reduced to arbitrarily small by deploying a sufficient number of random walks. Our algorithmic framework enables one to attain different trade-offs between the sample complexity (i.e., number of parallel random walks) and the mean square error of the statistical estimation. Also, the proposed bias reduction algorithm is generic and can be applied to optimize a large class of random walk sampling algorithms. To demonstrate the versatility of the framework, we apply it to optimize the Metropolis random walk and simple random walk sampling. Extensive experiments confirm the effectiveness and efficiency of our proposed algorithmic framework.

Finding the set of most influential users in online social networks (OSNs) to trigger the largest influence cascade is meaningful, e.g., companies may leverage the “word-of-mouth” effect to trigger a large cascade of purchases by offering free samples/discounts to those most influential users. This task is usually modeled as an influence maximization problem, and it has been widely studied in the past decade. However, considering that users in OSNs may participate in various online activities, e.g., joining discussion groups and commenting on same pages or products, influence diffusion through online activities becomes even more significant. In this article, we study the impact of online activities by formulating social-activity networks which contain both users and online activities, and thus induce two types of weighted edges, i.e., edges between users and edges between users and activities. To address the computation challenge, we define an influence centrality via random walks, and use the Monte Carlo framework to efficiently estimate the centrality. Furthermore, we develop a greedy-based algorithm with novel optimizations to find the most influential users for node recommendation. Experiments on real-world datasets show that our approach is very computationally efficient under different influence models, and also achieves larger influence spread by considering online activities.

Online product rating systems have become an indispensable component for numerous web services such as Amazon, eBay, Google Play Store, and TripAdvisor. One functionality of such systems is to uncover the product quality via product ratings (or reviews) contributed by consumers. However, a well-known psychological phenomenon called “ message-based persuasion ” lead to “ biased ” product ratings in a cascading manner (we call this the persuasion cascade ). This article investigates: (1) How does the persuasion cascade influence the product quality estimation accuracy? (2) Given a real-world product rating dataset, how to infer the persuasion cascade and analyze it to draw practical insights? We first develop a mathematical model to capture key factors of a persuasion cascade. We formulate a high-order Markov chain to characterize the opinion dynamics of a persuasion cascade and prove the convergence of opinions. We further bound the product quality estimation error for a class of rating aggregation rules including the averaging scoring rule, via the matrix perturbation theory and the Chernoff bound. We also design a maximum likelihood algorithm to infer parameters of the persuasion cascade. We conduct experiments on both synthetic data and real-world data from Amazon and TripAdvisor. Experiment results show that our inference algorithm has a high accuracy. Furthermore, persuasion cascades notably exist, but the average scoring rule has a small product quality estimation error under practical scenarios.

Persistent key-value (KV) stores are mainly designed based on the Log-Structured Merge-tree (LSM-tree), which suffer from large read and write amplifications, especially when KV stores grow in size. Existing design optimizations for LSM-tree-based KV stores often make certain trade-offs and fail to simultaneously improve both the read and write performance on large KV stores without sacrificing scan performance. We design UniKV, which unifies the key design ideas of hash indexing and the LSM-tree in a single system. Specifically, UniKV leverages data locality to differentiate the indexing management of KV pairs. It also develops multiple techniques to tackle the issues caused by unifying the indexing techniques, so as to simultaneously improve the performance in reads, writes, and scans. Experiments show that UniKV significantly outperforms several state-of-the-art KV stores (e.g., LevelDB, RocksDB, HyperLevelDB, and PebblesDB) in overall throughput under read-write mixed workloads.

Random walk is widely applied to sample large-scale graphs due to its simplicity of implementation and solid theoretical foundations of bias analysis. However, its computational efficiency is heavily limited by the slow convergence rate (a.k.a. long burn-in period). To address this issue, we propose a common neighbor aware random walk framework called CNARW, which leverages weighted walking by differentiating the next-hop candidate nodes to speed up the convergence. Specifically, CNARW takes into consideration the common neighbors between previously visited nodes and next-hop candidate nodes in each walking step. Based on CNARW, we further develop two efficient "unbiased sampling" schemes. Experimental results on real-world network datasets show that our approach converges remarkably faster than the state-of-the-art random walk sampling algorithms. Furthermore, to achieve the same estimation accuracy, our approach reduces the query cost (a measure of sampling budget) significantly. Lastly, we also use two case studies to demonstrate the effectiveness of our sampling framework in solving large-scale graph analysis tasks.

Graphlets are induced subgraph patterns and have been frequently applied to characterize the local topology structures of graphs across various domains, e.g., online social networks (OSNs) and biological networks. Discovering and computing graphlet statistics are highly challenging. First, the massive size of real-world graphs makes the exact computation of graphlets extremely expensive. Secondly, the graph topology may not be readily available so one has to resort to web crawling using the available application programming interfaces (APIs). In this work, we propose a general and novel framework to estimate graphlet statistics of " any size. " Our framework is based on collecting samples through consecutive steps of random walks. We derive an analytical bound on the sample size (via the Chernoff-Hoeffding technique) to guarantee the convergence of our unbiased estimator. To further improve the accuracy, we introduce two novel optimization techniques to reduce the lower bound on the sample size. Experimental evaluations demonstrate that our methods outperform the state-of-the-art method up to an order of magnitude both in terms of accuracy and time cost.