Graph Analytics Research Articles

Efficient Hop-constrained s-t Simple Path Enumeration

Graph is a ubiquitous structure representing entities and their relationships applied in many areas such as social networks, web graphs, and biological networks. One of the fundamental tasks in graph analytics is to investigate the relations between two vertices (e.g., users, items, and entities) such as how a vertex A influences another vertex B, or to what extent A and B are similar to each other, based on the graph topology structure. For this purpose, we study the problem of hop-constrained s-t simple path enumeration in this paper, which aims to list all simple paths from a source vertex s to a target vertex t with hop-constraint k. We first propose a polynomial delay algorithm, namely BC-DFS, based on a barrier-based pruning technique. Then, a join-oriented algorithm, namely JOIN, is designed to further enhance the query response time. On the theoretical side, BC-DFS is a polynomial delay algorithm with O(km) time per output where m is the number of edges in the graph. This time complexity is similar to the best known theoretical result for the polynomial delay algorithms of this problem. On the practical side, our comprehensive experiments on 15 real-life networks demonstrate the superior performance of the BC-DFS algorithm compared to the state-of-the-art techniques. It is also reported that the JOIN algorithm can further significantly enhance the query response time. In this paper, we also study the hop-constrained path enumeration problem with diversity constraint and propose a block-oriented algorithm, namely SCB. To further speed up the computation, hybrid lower bounds based on reverse shortest-path tree are also developed, namely SCB+. The experiments show our proposed methods significantly improve the query time and scalability comparing with baselines.

Graph diffusion distance: Properties and efficient computation.

We define a new family of similarity and distance measures on graphs, and explore their theoretical properties in comparison to conventional distance metrics. These measures are defined by the solution(s) to an optimization problem which attempts find a map minimizing the discrepancy between two graph Laplacian exponential matrices, under norm-preserving and sparsity constraints. Variants of the distance metric are introduced to consider such optimized maps under sparsity constraints as well as fixed time-scaling between the two Laplacians. The objective function of this optimization is multimodal and has discontinuous slope, and is hence difficult for univariate optimizers to solve. We demonstrate a novel procedure for efficiently calculating these optima for two of our distance measure variants. We present numerical experiments demonstrating that (a) upper bounds of our distance metrics can be used to distinguish between lineages of related graphs; (b) our procedure is faster at finding the required optima, by as much as a factor of 103; and (c) the upper bounds satisfy the triangle inequality exactly under some assumptions and approximately under others. We also derive an upper bound for the distance between two graph products, in terms of the distance between the two pairs of factors. Additionally, we present several possible applications, including the construction of infinite "graph limits" by means of Cauchy sequences of graphs related to one another by our distance measure.

Performance Evaluation of Intel Optane Memory for Managed Workloads

Intel Optane memory offers non-volatility, byte addressability, and high capacity. It suits managed workloads that prefer large main memory heaps. We investigate Optane as the main memory for managed (Java) workloads, focusing on performance scalability. As the workload (core count) increases, we note Optane’s performance relative to DRAM. A few workloads incur a slight slowdown on Optane memory, which helps conserve limited DRAM capacity. Unfortunately, other workloads scale poorly beyond a few core counts. This article investigates scaling bottlenecks for Java workloads on Optane memory, analyzing the application, runtime, and microarchitectural interactions. Poorly scaling workloads allocate objects rapidly and access objects in Optane memory frequently. These characteristics slow down the mutator and substantially slow down garbage collection (GC). At the microarchitecture level, load, store, and instruction miss penalties rise. To regain performance, we partition heaps across DRAM and Optane memory, a hybrid that scales considerably better than Optane alone. We exploit state-of-the-art GC approaches to partition heaps. Unfortunately, existing GC approaches needlessly waste DRAM capacity because they ignore runtime behavior. This article also introduces performance impact-guided memory allocation (PIMA) for hybrid memories. PIMA maximizes Optane utilization, allocating in DRAM only if it improves performance. It estimates the performance impact of allocating heaps in either memory type by sampling. We target PIMA at graph analytics workloads, offering a novel performance estimation method and detailed evaluation. PIMA identifies workload phases that benefit from DRAM with high (94.33%) accuracy, incurring only a 2% sampling overhead. PIMA operates stand-alone or combines with prior approaches to offer new performance versus DRAM capacity trade-offs. This work opens up Optane memory to a real-life role as the main memory for Java workloads.

Timestamped State Sharing for Stream Analytics

State access in existing distributed stream processing systems is restricted locally within each operator. However, in advanced stream analytics such as online learning and dynamic graph analytics, enabling state sharing across different operators makes application development easier and stream processing more efficient. In addition, when stream records are timestamped, proper time semantics should be defined for both state updates and fetches. We propose a new state abstraction to address the limitations of existing systems and develop a distributed stream processing system, Nova, with native support for timestamped state sharing. We validate the expressiveness and efficiency of Nova with extensive experiments.

Flows on measurable spaces

The theory of graph limits is only understood to a somewhat satisfactory degree in the cases of dense graphs and of bounded degree graphs. There is, however, a lot of interest in the intermediate cases. It appears that one of the most important constituents of graph limits in the general case will be Markov spaces (Markov chains on measurable spaces with a stationary distribution). This motivates our goal to extend some important theorems from finite graphs to Markov spaces or, more generally, to measurable spaces. In this paper, we show that much of flow theory, one of the most important areas in graph theory, can be extended to measurable spaces. Surprisingly, even the Markov space structure is not fully needed to get these results: all we need a standard Borel space with a measure on its square (generalizing the finite node set and the counting measure on the edge set). Our results may be considered as extensions of flow theory for directed graphs to the measurable case.

A Layout-Based Classification Method for Visualizing Time-Varying Graphs

Connectivity analysis between the components of large evolving systems can reveal significant patterns of interaction. The systems can be simulated by topological graph structures. However, such analysis becomes challenging on large and complex graphs. Tasks such as comparing, searching, and summarizing structures, are difficult due to the enormous number of calculations required. For time-varying graphs, the temporal dimension even intensifies the difficulty. In this article, we propose to reduce the complexity of analysis by focusing on subgraphs that are induced by closely related entities. To summarize the diverse structures of subgraphs, we build a supervised layout-based classification model. The main premise is that the graph structures can induce a unique appearance of the layout. In contrast to traditional graph theory-based and contemporary neural network-based methods of graph classification, our approach generates low costs and there is no need to learn informative graph representations. Combined with temporally stable visualizations, we can also facilitate the understanding of sub-structures and the tracking of graph evolution. The method is evaluated on two real-world datasets. The results show that our system is highly effective in carrying out visual-based analytics of large graphs.

Fast Core Maintenance in Dynamic Graphs

This article studies the core maintenance problem in dynamic graphs. The core number is a fundamental index reflecting the cohesiveness of a graph, which is widely used in large-scale graph analytics. The core maintenance problem requires updating the core numbers of vertices after a set of edges and vertices are inserted into or deleted from the graph. Previous works focus on the scenario of single-edge updates and process the edges one by one when multiple edges are inserted/deleted. We initiate the studies of processing multiple edges concurrently to improve the efficiency of core maintenance. Specifically, we discover a structure of inserted/deleted edges, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">superior edge set</i> , which can be processed together to greatly reduce unnecessarily repeated visits of vertices in the procedure of sequential edge processing. Based on the structure of the superior edge set, efficient algorithms are then devised for incremental and decremental core maintenance, respectively. Compared with single-edge processing algorithms, our algorithms show a significant speedup in the processing time. Furthermore, our algorithms admit parallel implementations, which can further improve the update efficiency. We also conduct extensive experiments on different types of real-world, temporal, and synthetic data sets, and the results illustrate that the proposed algorithms exhibit good efficiency, stability, and scalability.

HAM: Hotspot-Aware Manager for Improving Communications With 3D-Stacked Memory

Emerging High-Performance Computing (HPC) workloads, such as graph analytics, machine learning, and big data science, are data-intensive. Data-intensive workloads usually present fine-grained memory accesses with limited or no data locality, and thus incur frequent cache misses and low utilization of memory bandwidth. 3D-stacked memory devices such as Hybrid Memory Cube (HMC) and High Bandwidth Memory (HBM) can provide significantly higher bandwidth than conventional memory modules. However, the traditional interfaces and optimization methods for JEDEC DDR devices do not allow to fully exploit the potential performance of 3D-stacked memory with the massive amount of irregular memory accesses of data-intensive applications. In this article, we propose a novel Hotspot-Aware Manager (HAM) infrastructure for 3D-stacked memory devices capable of optimizing memory access streams via request aggregation, hotspot detection, and in-memory prefetching. We present the HAM design and implementation, and simulate it on a system using RISC-V embedded cores with attached HMC devices. We extensively evaluate HAM with over 12 benchmarks and applications representing diverse irregular memory access patterns. The results show that, on average, HAM reduces redundant requests by 37.51 percent and increases the prefetch buffer hit rate by 4.2 times, compared to a baseline streaming prefetcher. On the selected benchmark set, HAM provides performance gains of 21.81 percent in average (up to 34.28 percent), and power savings of 35.07 percent over a standard 3D-stacked memory.

Structure and influence in a global capital\u2013ownership network

Relationships between legal entities can be represented as a large weighted directed graph. In this work, we model the global capital ownership network across a hundred of millions of such entities with the goal of establishing a methodology for extracting and analysing meaningful patterns of capitalistic influence from the graph structure. To do so, we adapt and employ metrics from graph analytics and algorithms from the area of influence maximization. We characterize the relationships extracted and show that our analysis aligns with information from macro-economic studies; for example it recovers the presence of known tax heavens, which appear in dense subgraphs of countries. We also identify and quantify cases where capital is principally owned by others, corresponding to global influence. Beyond confirming known patterns and justifying our novel application of influence maximization methodology in this area, the outcome also offers new insight and metrics in this domain, by highlighting the existence of strong communities of capitalistic property. We leverage influence maximization methods as a means to evaluate the impact of entities in these contexts. Finally we formulate the results of our study into recommendations for future analyses of this kind.

Network analysis of earthquake ground motion spatial correlation: a case study with the San Jacinto seismic nodal array

SUMMARYThe spatial correlation of earthquake ground motion intensity can be measured from strong motion data; however, the data used in past studies is sparsely sampled in space, and only the interstation distance was considered as a correlation variable. These limitations mean that we have only weak constraints on the true correlation structure of ground motion and that potentially important aspects of spatial correlation are unconstrained. In this study, we combine a large-N seismic array and graph analytics to explore this issue at a local scale using small local and regional earthquakes. Our result suggests site conditions, and how they interact with the incident seismic wavefield, strongly condition the spatial correlation of ground motion. Future progress in characterizing ground motion spatial variability will require dense wavefield measurements, either through nodal deployments, or perhaps distributed acoustic sensing measurements, of seismic wavefields. Aftershock sequences of major earthquakes would provide particularly data-rich targets of opportunity.

Svelto: High-Level Synthesis of Multi-Threaded Accelerators for Graph Analytics

Graph analytics are an emerging class of irregular applications. Operating on very large datasets, they present unique behaviors, such as fine-grained, unpredictable memory accesses, and highly unbalanced task level parallelism, that make existing high-performance general-purpose processors or accelerators (e.g., GPUs) suboptimal. To address these issues, research and industry are developing a variety of custom accelerator designs for this application area, including solutions based on reconfigurable devices (Field Programmable Gate Arrays). These new approaches often employ High-Level Synthesis (HLS) to Speed up the development of the accelerators. In this paper, we propose a novel architecture template for the automatic generation of accelerators for graph analytics and irregular applications. The architecture template includes a dynamic task scheduling mechanism, a parallel array of accelerators that enables supporting task-level parallelism with context switching, and a related multi-channel memory interface that decouples communication from computation and provides support for fine-grained atomic memory operations. We discuss the integration of the architectural template in an HLS flow, presenting the necessary modifications to enable automatic generation of the custom architectures starting from OpenMP annotated code. We evaluate our approach first by synthesizing and exploring triangle counting, a common graph algorithm, and then by synthesizing custom designs for a set of graph database benchmark queries, representing series of graph pattern matching routines. We compare the synthesized accelerators with previous state-of-the-art methodologies for the synthesis of parallel architectures, showing that the proposed approach allows reducing resource usage by optimizing the number of accelerators replicas without any performance penalty.

Gretch

Data-dependent memory accesses (DDAs) pose an important challenge for high-performance graph analytics (GA). This is because such memory accesses do not exhibit enough temporal and spatial locality resulting in low cache performance. Prior efforts that focused on improving the performance of DDAs for GA are not applicable across various GA frameworks. This is because (1) they only focus on one particular graph representation, and (2) they require workload changes to communicate specific information to the hardware for their effective operation. In this work, we propose a hardware-only solution to improving the performance of DDAs for GA across multiple GA frameworks. We present a hardware prefetcher for GA called Gretch, that addresses the above limitations. An important observation we make is that identifying certain DDAs without hardware-software communication is sensitive to the instruction scheduling. A key contribution of this work is a hardware mechanism that activates Gretch to identify DDAs when using either in-order or out-of-order instruction scheduling. Our evaluation shows that Gretch provides an average speedup of 38% over no prefetching, 25% over conventional stride prefetcher, and outperforms prior DDAs prefetchers by 22% with only 1% increase in power consumption when executed on different GA workloads and frameworks.

On the Curvature Energy of Cartesian Surfaces

We analyze the lower semicontinuous envelope of the curvature functional of Cartesian surfaces in codimension one. To this aim, following the approach by Anzellotti–Serapioni–Tamanini, we study the class of currents that naturally arise as weak limits of Gauss graphs of smooth functions. The curvature measures are then studied in the non-parametric case. Concerning homogeneous functions, some model examples are studied in detail. Finally, a new gap phenomenon is observed.

Automatic detection of influential actors in disinformation networks

The weaponization of digital communications and social media to conduct disinformation campaigns at immense scale, speed, and reach presents new challenges to identify and counter hostile influence operations (IOs). This paper presents an end-to-end framework to automate detection of disinformation narratives, networks, and influential actors. The framework integrates natural language processing, machine learning, graph analytics, and a network causal inference approach to quantify the impact of individual actors in spreading IO narratives. We demonstrate its capability on real-world hostile IO campaigns with Twitter datasets collected during the 2017 French presidential elections and known IO accounts disclosed by Twitter over a broad range of IO campaigns (May 2007 to February 2020), over 50,000 accounts, 17 countries, and different account types including both trolls and bots. Our system detects IO accounts with 96% precision, 79% recall, and 96% area-under-the precision-recall (P-R) curve; maps out salient network communities; and discovers high-impact accounts that escape the lens of traditional impact statistics based on activity counts and network centrality. Results are corroborated with independent sources of known IO accounts from US Congressional reports, investigative journalism, and IO datasets provided by Twitter.

Harmonic analysis of symmetric random graphs

This note attempts to understand graph limits as defined by Lovasz and Szegedy (2006)} in terms of harmonic analysis on semigroups. This is done by representing probability distributions of random exchangeable graphs as mixtures of characters on the semigroup of unlabeled graphs with node-disjoint union, thereby providing an alternative derivation of de Finetti's theorem for random exchangeable graphs.

Minimal definable graphs of definable chromatic number at least three

Abstract We show that there is a Borel graph on a standard Borel space of Borel chromatic number three that admits a Borel homomorphism to every analytic graph on a standard Borel space of Borel chromatic number at least three. Moreover, we characterize the Borel graphs on standard Borel spaces of vertex-degree at most two with this property and show that the analogous result for digraphs fails.

Equitable colourings of Borel graphs

Abstract Hajnal and Szemerédi proved that if G is a finite graph with maximum degree $\Delta $ , then for every integer $k \geq \Delta +1$ , G has a proper colouring with k colours in which every two colour classes differ in size at most by $1$ ; such colourings are called equitable. We obtain an analogue of this result for infinite graphs in the Borel setting. Specifically, we show that if G is an aperiodic Borel graph of finite maximum degree $\Delta $ , then for each $k \geq \Delta + 1$ , G has a Borel proper k-colouring in which every two colour classes are related by an element of the Borel full semigroup of G. In particular, such colourings are equitable with respect to every G-invariant probability measure. We also establish a measurable version of a result of Kostochka and Nakprasit on equitable $\Delta $ -colourings of graphs with small average degree. Namely, we prove that if $\Delta \geq 3$ , G does not contain a clique on $\Delta + 1$ vertices and $\mu $ is an atomless G-invariant probability measure such that the average degree of G with respect to $\mu $ is at most $\Delta /5$ , then G has a $\mu $ -equitable $\Delta $ -colouring. As steps toward the proof of this result, we establish measurable and list-colouring extensions of a strengthening of Brooks’ theorem due to Kostochka and Nakprasit.

Understanding Graph Embedding Methods and Their Applications

Graph analytics can lead to better quantitative understanding and control of complex networks, but traditional methods suffer from the high computational cost and excessive memory requirements asso...

Graph Sampling with Distributed In-Memory Dataflow Systems.

Given a large graph, a graph sample determines a subgraph with similar characteristics for certain metrics of the original graph. The samples are much smaller thereby accelerating and simplifying the analysis and visualization of large graphs. We focus on the implementation of distributed graph sampling for Big Data frameworks and in-memory dataflow systems such as Apache Spark or Apache Flink. We evaluate the scalability of the new implementations and analyze to what degree the sampling approaches preserve certain graph metrics compared to the original graph. The latter analysis also uses comparative graph visualizations. The presented methods will be open source and be integrated into Gradoop, a system for distributed graph analytics.

Higher-order fluctuations in dense random graph models

Our main results are quantitative bounds in the multivariate normal approximation of centred subgraph counts in random graphs generated by a general graphon and independent vertex labels. We are interested in these statistics because they are key to understanding fluctuations of regular subgraph counts — a cornerstone of dense graph limit theory. We also identify the resulting limiting Gaussian stochastic measures by means of the theory of generalised U-statistics and Gaussian Hilbert spaces, which we think is a suitable framework to describe and understand higher-order fluctuations in dense random graph models. With this article, we believe we answer the question “What is the central limit theorem of dense graph limit theory?”. We complement the theory with some statistical applications to illustrate the use of centred subgraph counts in network modelling.