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HyperHeadTail is a streaming algorithm for estimating the degree distribution of a graph from a stream of edges using very small storage space. Our algorithm builds upon the HeadTail algorithm of Simpson, Comandur, and McGregor [14], but extends it to handle repeat edges and variable-length sliding time windows, making it suitable for application to real-world streams such as those generated by network traffic or other communication networks.
Non-volatile main memory (NVRAM) technologies provide an attractive set of features for large-scale graph analytics, including byte-addressability, low idle power, and improved memory-density. NVRAM systems today have an order of magnitude more NVRAM than traditional memory (DRAM). NVRAM systems could therefore potentially allow very large graph problems to be solved on a single machine, at a modest cost. However, a significant challenge in achieving high performance is in accounting for the fact that NVRAM writes can be much more expensive than NVRAM reads. In this paper, we propose an approach to parallel graph analytics using the Parallel Semi-Asymmetric Model (PSAM), in which the graph is stored as a read-only data structure (in NVRAM), and the amount of mutable memory is kept proportional to the number of vertices. Similar to the popular semi-external and semi-streaming models for graph analytics, the PSAM approach assumes that the vertices of the graph fit in a fast read-write memory (DRAM), but the edges do not. In NVRAM systems, our approach eliminates writes to the NVRAM, among other benefits. To experimentally study this new setting, we develop Sage, a parallel semi-asymmetric graph engine with which we implement provably-efficient (and often work-optimal) PSAM algorithms for over a dozen fundamental graph problems. We experimentally study Sage using a 48--core machine on the largest publicly-available real-world graph (the Hyperlink Web graph with over 3.5 billion vertices and 128 billion edges) equipped with Optane DC Persistent Memory, and show that Sage outperforms the fastest prior systems designed for NVRAM. Importantly, we also show that Sage nearly matches the fastest prior systems running solely in DRAM, by effectively hiding the costs of repeatedly accessing NVRAM versus DRAM.
Graph algorithms with polynomial space and time requirements often become infeasible for massive graphs with billions of edges or more. State-of-the-art approaches therefore employ approximate serial, parallel, and distributed algorithms to tackle these challenges. However, such approaches require storing the entire graph in memory and thus need access to costly computing resources such as clusters and supercomputers. In this paper, we present practical streaming approaches for solving massive graph problems using limited memory for two prototypical graph problems: maximum weighted matching and minimum weighted edge cover. For matching, we conduct a thorough computational study on two of the semi-streaming algorithms including a recent breakthrough result that achieves a $1/(2+\varepsilon)$-approximation of the weight while using $O( n \log W /\epsilon)$ memory (here $n$ is the number of vertices and $W$ is the maximum edge weight), designed by Paz and Schwartzman [SODA, 2017]. Empirically, we show that the semi-streaming algorithms produce matchings whose weight is close to the best $1/2$-approximate offline algorithm while requiring less time and an order-of-magnitude less memory. For minimum weighted edge cover, we develop three novel semi-streaming algorithms. Two of these algorithms require a single pass through the input graph, require $O(n \log n)$ memory, and provide a 2-approximation guarantee on the objective. We also leverage a relationship between approximate maximum weighted matching and approximate minimum weighted edge cover to develop a two-pass $3/2+\epsilon$-approximate algorithm with the memory requirement of Paz and Schwartzman's semi-streaming matching algorithm. These streaming approaches are compared against the state-of-the-art 3/2-approximate offline algorithm. The semi-streaming matching and the novel edge cover algorithms proposed in this paper can process graphs with several billions of edges in under 30 minutes using 6 GB of memory, which is at least an order of magnitude improvement from the offline (non-streaming) algorithms. For the largest graph, the best alternative offline parallel approximation algorithm (GPA+ROMA) could not finish in three hours even while employing hundreds of processors and 1 TB of memory. We also demonstrate an application of the semi-streaming algorithm by computing a matching using linearly bounded memory on item intersection graphs derived from three machine learning datasets, whereas the existing offline algorithms could not complete on one of these datasets since their memory requirements exceeded 1TB.
With the prevalence of the World Wide Web and social networks, there has been a growing interest in high performance analytics for constantly-evolving dynamic graphs. Modern GPUs provide massive AQ1 amount of parallelism for efficient graph processing, but the challenges remain due to their lack of support for the near real-time streaming nature of dynamic graphs. Specifically, due to the current high volume and velocity of graph data combined with the complexity of user queries, traditional processing methods by first storing the updates and then repeatedly running static graph analytics on a sequence of versions or snapshots are deemed undesirable and computational infeasible on GPU. We present EvoGraph, a highly efficient and scalable GPU- based dynamic graph analytics framework.
Graphs are a widely used abstraction for representing a variety of important real-world problems including emulating cyber networks for situational awareness, or studying social networks to understand human interactions or pandemic spread. Communication data is often converted into graphs to help understand social and technical patterns in the underlying communication data. However, prior to this project, little work had been performed analyzing how best to develop graphs from such data. Thus, many critical, national security problems were being performed against graph representations of questionable quality. Herein, we describe our analyses that were precursors to our final statistically grounded technique for creating static graph snapshots from a stream of communication events. The first analyzes the statistical distribution properties of a variety of real-world communication datasets generally fit best by Pareto, log normal, and extreme value distributions. The second derives graph properties that can be estimated given the expected statistical distribution for communication events and the communication interval to be viewed node observability, edge observability, and expected accuracy of node degree. Unfortunately, as that final process is under review for publication, we can't publish it here at this time.
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Stream temperature is a fundamental control on ecosystem health. Recent efforts incorporating process guidance into deep learning models for predicting stream temperature have been shown to outperform existing statistical and physical models. This performance is in part because deep learning architectures can actively learn spatiotemporal relationships that govern how water and energy propagate through a river network. However, exploration of how spatiotemporal awareness and process guidance influence a model's generalizability under shifting environmental conditions such as climate change is limited. Here, we use Explainable Artificial Intelligence (XAI) to interrogate how differing deep learning architectures affect a model's learned spatial and temporal dependencies, and how those learned dependencies affect a model's ability to maintain high accuracy when applied to unseen environmental conditions. Using the Delaware River Basin in the northeastern United States as a test case, we compare two spatiotemporally aware process–guided deep learning models for predicting stream temperature (a recurrent graph convolution network—RGCN, and a temporal convolution graph model—Graph WaveNet). Both models achieve equally high predictive performance when testing data are well represented in the training data (test root mean squared errors of 1.64°C and 1.65°C); however, Graph WaveNet significantly outperforms RGCN in 4 out of 5 experiments where test partitions represent different types of unseen environmental conditions. XAI results show that the architecture of Graph WaveNet leads to learned spatial relationships with greater fidelity to physical processes, and that this fidelity improves the generalizability of the model when applied to shifting and/or unseen environmental conditions.
Graph clustering, popularly known as community detection, is a fundamental graph operation used in several applications of relevance for network analysis and cybersecurity. Community detection is an operation of partitioning a network into an arbitrary number of “communities” such that each com munity represents a tightly-knit group of nodes with relatively sparser connections to the rest of the nodes in the network. The need to compute clustering on large-scale networks necessitates the development of efficient parallel algorithms capable of exploiting modern parallel architectures. However, due to their irregular and inherently sequential nature, many of the current algorithms for community detection are challenging to parallelize. In response to the 2018 Graph Challenge, we present Vite which is a distributed-memory parallel community detection method. Vite is a parallelization of the algorithmic template provided by a widely-used serial method (Louvain). Alongside, it uses several heuristics aimed at significantly improving parallelism and performance, while preserving output quality. Using the inputs from the 2018 Graph Challenge (static and streaming), we demonstrate superior performance and high quality solutions based on four parallelization heuristics.
Code developed in conjunction with a research paper. This code demonstrates how to identify static graph snapshots from a stream of communication events. A second, related code generates simulated communication events with known split moments for accuracy testing.SAND2020-12245 M Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA0003525.
Schematics are given for test section configurations, orifice configurations, and the dilution jet mixing test rig used to collect a data base on mixing a single sided and a two sided row of jets with a confined cross flow. Parameters investigated include momentum ratio; nonuniform cross stream temperature and velocity profiles; cold/hot injection, and cross stream flow area convergence. Graphs show measured theta momentum distributions for: (1) in line and staggered orifice configurations; and (2) the profiled mainstream; and (3) flow area convergence.
The purpose of this project was to develop sampling-based algorithms to discover hidden struc- ture in massive data sets. Inferring structure in large data sets is an increasingly common task in many critical national security applications. These data sets come from myriad sources, such as network traffic, sensor data, and data generated by large-scale simulations. They are often so large that traditional data mining techniques are time consuming or even infeasible. To address this problem, we focus on a class of algorithms that do not compute an exact answer, but instead use sampling to compute an approximate answer using fewer resources. The particular class of algorithms that we focus on are streaming algorithms , so called because they are designed to handle high-throughput streams of data. Streaming algorithms have only a small amount of working storage - much less than the size of the full data stream - so they must necessarily use sampling to approximate the correct answer. We present two results: * A streaming algorithm called HyperHeadTail , that estimates the degree distribution of a graph (i.e., the distribution of the number of connections for each node in a network). The degree distribution is a fundamental graph property, but prior work on estimating the degree distribution in a streaming setting was impractical for many real-world application. We improve upon prior work by developing an algorithm that can handle streams with repeated edges, and graph structures that evolve over time. * An algorithm for the task of maintaining a weighted subsample of items in a stream, when the items must be sampled according to their weight, and the weights are dynamically changing. To our knowledge, this is the first such algorithm designed for dynamically evolving weights. We expect it may be useful as a building block for other streaming algorithms on dynamic data sets.
The Emu Chick prototype implements migratory memory-side processing in a novel hardware system. Rather than transferring large amounts of data across the system interconnect, the Emu Chick moves lightweight thread contexts to near-memory cores before the beginning of each remote memory read. Previous work has characterized the performance of the Chick prototype in terms of memory bandwidth and programming differences from more typical, non-migratory platforms, but there has not yet been an analysis of algorithms on this system. This work evaluates irregular algorithms that could benefit from the lightweight, memory-side processing of the Chick and demonstrates techniques and optimization strategies for achieving performance in sparse matrix-vector multiply operation (SpMV), breadth-first search (BFS), and graph alignment across up to eight distributed nodes encompassing 64 nodelets in the Chick system. We also define and justify relative metrics to compare prototype FPGA-based hardware with established ASIC architectures. The Chick currently supports up to 68x scaling for graph alignment, 80 MTEPS for BFS on balanced graphs, and 50% of measured STREAM bandwidth for SpMV.
SRI International (SRI) has developed an improved queueing algorithm, known as Stochastic Fairness Queueing (SFQ), for best-effort traffic (i.e., traffic that does not require any guaranteed service). SFQ is a probablistic variant of strict fair queueing where instead of a single queue being allocated per flow, a fixed number of queues are used and a hash function maps the IP source and destination to a particular queue. A seed to the hash function is also perturbed occasionally to help distribute the flows amongst different queues when more than one flow maps to the same queue during the lifetime of the flow. SFQ provides 'fair' access by trying to ensure that each flow from source to destination host obtains equal access to the available bandwidth. This report covers a series of experiments performed on DARTnet evaluating the behavior and performance of SFQ against a FIFO queueing discipline. These experiments were designed to show SFQ's advantages and performance, and include tests demonstrating: Fair utilization of available resources; Starvation prevention; Graceful degradation under overload conditions; and Resource usage. In general, the experiments do show that SFQ is better than FIFO queueing at allocating bandwidth equally among a set of flows. SFQ also prevents a stream from dominating the available bandwidth, which seems to be a tendency with FIFO queueing (i.e., if a flow demands more than its share of the available bandwidth, with FIFO queueing that stream receives a disproportionate amount when compared to flows demanding less than their share). Furthermore, SFQ seems to reward 'nice' users of the network by providing a lower variance in delay and more throughput when their resource demand is less than their available share. Both SFQ and FIFO queueing seem to degrade fairly well as the network becomes saturated and to recover well as the network becomes less congested. Not unexpectedly, FIFO queueing is a little more efficient than SFQ-the delays are less and the throughput slightly higher because SFQ requires more processing. However, the performance difference between the two queueing disciplines is relatively small. However, the experiments do point out some interesting behavior. FIFO queueing can behave better than SFQ with seed perturbation. We recommend further evaluation of the hash function and the seed perturbation technique. There are probably weaknesses in their current selection that cause this unexpected behavior. SFQ also seems to possess good scaling properties. To verify this, more experiments with a larger number of streams from more hosts need to be executed and examined, including the staggered introduction of streams. Staggering the streams may prove important, because graphs in the degradation experiment revealed some unexpected increases and decreases in throughput, which should be examined. This may again be due to the interaction of the hash function with the seed perturbation but it may also be related to some other unknown problem.
Solar and interplanetary data are examined, taking into account the identification of the heliographic longitudes of the coronal source regions of high speed solar wind (SW) streams by Nolte and Roelof (1973). Nolte and Roelof have 'mapped' the velocities measured near earth back to the sun using the approximation of constant radial velocity. The 'Carrington carpet' for rotations 1597-1616 is shown in a graph. Coronal sources of high speed streams appear in the form of solid black areas. The contours of the stream sources are laid on 'evolutionary charts' of solar active region histories for the Southern and Northern Hemispheres. Questions regarding the interplay of active regions and solar wind are investigated, giving attention to developments during the years 1973, 1974, and 1975.
This report summarizes the work performed under the Sandia LDRD project "Adverse Event Prediction Using Graph-Augmented Temporal Analysis." The goal of the project was to develop a method for analyzing multiple time-series data streams to identify precursors providing advance warning of the potential occurrence of events of interest. The proposed approach combined temporal analysis of each data stream with reasoning about relationships between data streams using a geospatial-temporal semantic graph. This class of problems is relevant to several important topics of national interest. In the course of this work we developed new temporal analysis techniques, including temporal analysis using Markov Chain Monte Carlo techniques, temporal shift algorithms to refine forecasts, and a version of Ripley's K-function extended to support temporal precursor identification. This report summarizes the project's major accomplishments, and gathers the abstracts and references for the publication submissions and reports that were prepared as part of this work. We then describe work in progress that is not yet ready for publication.
This report summarizes the work performed under the Sandia LDRD project "Adverse Event Prediction Using Graph-Augmented Temporal Analysis." The goal of the project was to develop a method for analyzing multiple time-series data streams to identify precursors providing advance warning of the potential occurrence of events of interest. The proposed approach combined temporal analysis of each data stream with reasoning about relationships between data streams using a geospatial-temporal semantic graph. This class of problems is relevant to several important topics of national interest. In the course of this work we developed new temporal analysis techniques, including temporal analysis using Markov Chain Monte Carlo techniques, temporal shift algorithms to refine forecasts, and a version of Ripley's K-function extended to support temporal precursor identification. This report summarizes the project's major accomplishments, and gathers the abstracts and references for the publication sub-missions and reports that were prepared as part of this work. We then describe work in progress that is not yet ready for publication.
A query graph, which includes vertices and edges, represents a query on graph-structured data. The query graph is decomposed into query subgraphs. A network analysis tool performs continuous subgraph matching queries to facilitate analysis of computer network traffic, social media events, or other streams of data represented as a dynamic data graph (graph-structured data). This can help identify emerging trends in the data. Some features of the network analysis tool enhance performance by effectively utilizing distributed computing resources (including processing cores and memory at different nodes of a cluster) to speed up the process of updating the dynamic data graph and detecting matches of query subgraphs. Features of a query graph building tool enhance usability by providing intuitive ways to specify query graphs and their subgraphs. Features of a results visualization tool enhance usability by providing an intuitive way to present the results of continuous subgraph matching queries.
Here, we present the design and optimization of a solver for efficient and high-throughput computation of the marginalized graph kernel on General Purpose GPUs. The graph kernel is computed using the conjugate gradient method to solve a generalized Laplacian of the tensor product between a pair of graphs. To cope with the large gap between the instruction throughput and the memory bandwidth of the GPUs, our solver forms the graph tensor product on-the-fly without storing it in memory. This is achieved by using threads in a warp cooperatively to stream the adjacency and edge label matrices of individual graphs by small square matrix blocks called tiles, which are then staged in registers and the shared memory for later reuse. Warps across a thread block can further share tiles via the shared memory to increase data reuse. We exploit the sparsity of the graphs hierarchically by storing only non-empty tiles using a coordinate format and nonzero elements within each tile using bitmaps. We propose a new partition-based reordering algorithm for aggregating nonzero elements of the graphs into fewer but denser tiles to further exploit sparsity. We carry out extensive theoretical analyses on the graph tensor product primitives for tiles of various density and evaluate their performance on synthetic and real-world datasets. Our solver delivers three to four orders of magnitude speedup over existing CPU-based solvers such as GraKeL and GraphKernels. The capability of the solver enables kernel-based learning tasks at unprecedented scales.