Graph partitioning is an important preprocessing step to distributed graph processing. In edge partitioning, the edge set of a given graph is split into $k$ equally-sized partitions, such that the replication of vertices across partitions is minimized. Streaming is a viable approach to partition graphs that exceed the memory capacities of a single server. The graph is ingested as a stream of edges, and one edge at a time is immediately and irrevocably assigned to a partition based on a scoring function. However, streaming partitioning suffers from the uninformed assignment problem: At the time of partitioning early edges in the stream, there is no information available about the rest of the edges. As a consequence, edge assignments are often driven by balancing considerations, and the achieved replication factor is comparably high. In this paper, we propose 2PS, a novel two-phase streaming algorithm for high-quality edge partitioning. In the first phase, vertices are separated into clusters by a lightweight streaming clustering algorithm. In the second phase, the graph is re-streamed and edge partitioning is performed while taking into account the clustering of the vertices from the first phase. Our evaluations show that 2PS can achieve a replication factor that is comparable to heavy-weight random access partitioners while inducing orders of magnitude lower memory overhead.
In recent years, the graph partitioning problem gained importance as a mandatory preprocessing step for distributed graph processing on very large graphs. Existing graph partitioning algorithms minimize partitioning latency by assigning individual graph edges to partitions in a streaming manner --- at the cost of reduced partitioning quality. However, we argue that the mere minimization of partitioning latency is not the optimal design choice in terms of minimizing total graph analysis latency, i.e., the sum of partitioning and processing latency. Instead, for complex and long-running graph pr…
Graph edge partitioning is an important preprocessing step to optimize distributed computing jobs on graph-structured data. The edge set of a given graph is split into $k$ equally-sized partitions, such that the replication of vertices across partitions is minimized. Out-of-core edge partitioning algorithms are able to tackle the problem with low memory overhead. Exsisting out-of-core algorithms mainly work in a streaming manner and can be grouped into two types. While \emph{stateless} streaming edge partitioning is fast and yields low partitioning quality, stateful streaming edge partitioning…
When processing data streams with highly skewed and nonstationary key distributions, we often observe overloaded partitions when the hash partitioning fails to balance data correctly. To avoid slow tasks that delay the completion of the whole stage of computation, it is necessary to apply adaptive, on-the-fly partitioning that continuously recomputes an optimal partitioner, given the observed key distribution. While such solutions exist for batch processing of static data sets and stateless stream processing, the task is difficult for long-running stateful streaming jobs where key distribution…
Distributed systems that manage and process graph-structured data internally solve a graph partitioning problem to minimize their communication overhead and query run-time. Besides computational complexity -- optimal graph partitioning is NP-hard -- another important consideration is the memory overhead. Real-world graphs often have an immense size, such that loading the complete graph into memory for partitioning is not economical or feasible. Currently, the common approach to reduce memory overhead is to rely on streaming partitioning algorithms. While the latest streaming algorithms lead to…
Partitioning a graph into balanced blocks such that few edges run between blocks is a key problem for large-scale distributed processing. A current trend for partitioning huge graphs are streaming algorithms, which use low computational resources. In this work, we present a shared-memory streaming multi-recursive partitioning scheme that performs recursive multi-sections on the fly without knowing the overall input graph. Our approach has a considerably lower running time complexity in comparison with state-of-the-art non-buffered one-pass partitioning algorithms for the standard graph partiti…
Graph partitioning plays a vital role in distributedlarge-scale web graph analytics, such as pagerank and labelpropagation. The quality and scalability of partitioning strategyhave a strong impact on such communication- and computation-intensive applications, since it drives the communication costand the workload balance among distributed computing nodes.Recently, the streaming model shows promise in optimizing graphpartitioning. However, existing streaming partitioning strategieseither lack of adequate quality or fall short in scaling with alarge number of partitions.In this work, we explore …
The sheer increase in the size of graph data has created a lot of interest into developing efficient distributed graph processing frameworks. Popular existing frameworks such as Graphlab and Pregel rely on balanced graph partitioning in order to minimize communication and achieve work balance. In this work we contribute to the recent research line of streaming graph partitioning \cite{stantonstreaming,stanton,fennel} which computes an approximately balanced $k$-partitioning of the vertex set of a graph using a single pass over the graph stream using degree-based criteria. This graph partitioni…
One standard solution for analyzing large natural graphs is to adopt distributed computation on clusters. In distributed computation, graph partitioning (GP) methods assign the vertices or edges of a graph to different machines in a balanced way so that some distributed algorithms can be adapted for. Most of traditional GP methods are offline, which means that the whole graph has been observed before partitioning. However, the offline methods often incur high computation cost. Hence, streaming graph partitioning (SGP) methods, which can partition graphs in an online way, have recently attracte…
Many well-known, real-world problems involve dynamic data which describe the relationship among the entities. Hypergraphs are powerful combinatorial structures that are frequently used to model such data. For many of today's data-centric applications, this data is streaming; new items arrive continuously, and the data grows with time. With paradigms such as Internet of Things and Edge Computing, such applications become more natural and more practical. In this work, we assume a streaming model where the data is modeled as a hypergraph, which is generated at the edge. This data then partitioned…
Time-evolving large graph has received attention due to their participation in real-world applications such as social networks and PageRank calculation. It is necessary to partition a large-scale dynamic graph in a streaming manner to overcome the memory bottleneck while partitioning the computational load. Reducing network communication and balancing the load between the partitions are the criteria to achieve effective run-time performance in graph partitioning. Moreover, an optimal resource allocation is needed to utilise the resources while catering the graph streams into the partitions. A …
We introduce XtraPuLP, a new distributed-memory graph partitioner designed to process trillion-edge graphs. XtraPuLP is based on the scalable label propagation community detection technique, which has been demonstrated as a viable means to produce high quality partitions with minimal computation time. On a collection of large sparse graphs, we show that XtraPuLP partitioning quality is comparable to state-of-the-art partitioning methods. We also demonstrate that XtraPuLP can produce partitions of real-world graphs with billion+ vertices in minutes. Further, we show that using XtraPuLP partitio…
The availability of larger and larger graph datasets, growing exponentially over the years, has created several new algorithmic challenges to be addressed. Sequential approaches have become unfeasible, while interest on parallel and distributed algorithms has greatly increased. Appropriately partitioning the graph as a preprocessing step can improve the degree of parallelism of its analysis. A number of heuristic algorithms have been developed to solve this problem, but many of them subdivide the graph on its vertex set, thus obtaining a vertex-partitioned graph. Aim of this paper is to explor…
Graph partitioning drives graph processing in distributed, disk-based and NUMA-aware systems. A commonly used partitioning goal is to balance the number of edges per partition in conjunction with minimizing the edge or vertex cut. While this type of partitioning is computationally expensive, we observe that such topology-driven partitioning nonetheless results in computational load imbalance. We propose Vertex- and Edge-Balanced Ordering (VEBO): balance the number of edges and the number of unique destinations of those edges. VEBO optimally balances edges and vertices for graphs with a power-l…
We study the problem of load balancing in distributed stream processing engines, which is exacerbated in the presence of skew. We introduce Partial Key Grouping (PKG), a new stream partitioning scheme that adapts the classical "power of two choices" to a distributed streaming setting by leveraging two novel techniques: key splitting and local load estimation. In so doing, it achieves better load balancing than key grouping while being more scalable than shuffle grouping. We test PKG on several large datasets, both real-world and synthetic. Compared to standard hashing, PKG reduces the load imb…
In recent years, with the rapid development of sensing technology and the Internet of Things (IoT), sensors play increasingly important roles in traffic control, medical monitoring, industrial production and etc. They generated high volume of data in a streaming way that often need to be processed in real time. Therefore, streaming data computing technology plays an indispensable role in the real-time processing of sensor data in high throughput but low latency. In view of the above problems, the proposed framework is implemented on top of Spark Streaming, which builds up a gray model based tr…
Leiden University（莱顿大学）；University of Amsterdam（阿姆斯特丹大学）
Nowadays, many AI applications utilizing resource-constrained edge devices (e.g., small mobile robots, tiny IoT devices, etc.) require Convolutional Neural Network (CNN) inference on a distributed system at the edge due to limited resources of a single edge device to accommodate and execute a large CNN. There are four main partitioning strategies that can be utilized to partition a large CNN model and perform distributed CNN inference on multiple devices at the edge. However, to the best of our knowledge, no research has been conducted to investigate how these four partitioning strategies affe…
Edge-centric distributed computations have appeared as a recent technique to improve the shortcomings of think-like-a-vertex algorithms on large scale-free networks. In order to increase parallelism on this model, edge partitioning - partitioning edges into roughly equally sized blocks - has emerged as an alternative to traditional (node-based) graph partitioning. In this work, we give a distributed memory parallel algorithm to compute high-quality edge partitions in a scalable way. Our algorithm scales to networks with billions of edges, and runs efficiently on thousands of PEs. Our technique…
Partitioning an input graph over a set of workers is a complex operation. Objectives are twofold: split the work evenly, so that every worker gets an equal share, and minimize edge cut to achieve a good work locality (i.e. workers can work independently). Partitioning a graph accessible from memory is a notorious NP-complete problem. Motivated by the regain of interest for the stream processing paradigm (where nodes and edges arrive as a flow to the datacenter), we propose in this paper a stream-enabled graph partitioning system that constantly seeks an optimum between those two objectives. We…
Many real-world systems, such as social networks, rely on mining efficiently large graphs, with hundreds of millions of vertices and edges. This volume of information requires partitioning the graph across multiple nodes in a distributed system. This has a deep effect on performance, as traversing edges cut between partitions incurs a significant performance penalty due to the cost of communication. Thus, several systems in the literature have attempted to improve computational performance by enhancing graph partitioning, but they do not support another characteristic of real-world graphs: gra…
We propose Distributed Neighbor Expansion (Distributed NE), a parallel and distributed graph partitioning method that can scale to trillion-edge graphs while providing high partitioning quality. Distributed NE is based on a new heuristic, called parallel expansion, where each partition is constructed in parallel by greedily expanding its edge set from a single vertex in such a way that the increase of the vertex cuts becomes local minimal. We theoretically prove that the proposed method has the upper bound in the partitioning quality. The empirical evaluation with various graphs shows that the…
A directed acyclic hypergraph is a generalized concept of a directed acyclic graph, where each hyperedge can contain an arbitrary number of tails and heads. Directed hypergraphs can be used to model data flow and execution dependencies in streaming applications. Thus, hypergraph partitioning algorithms can be used to obtain efficient parallelizations for multiprocessor architectures. However, an acyclicity constraint on the partition is necessary when mapping streaming applications to embedded multiprocessors due to resource restrictions on this type of hardware. The acyclic hypergraph partiti…
We propose a way of preventing race conditions in the evaluation of the surface integral contribution in discontinuous Galerkin and finite volume flow solvers by coloring the edges (or faces) of the computational mesh. In this work we use a partitioning algorithm that separates the edges of triangular elements into three groups and the faces of quadrangular and tetrahedral elements into four groups; we then extend this partitioning to adaptively refined, nonconforming meshes. We use the ascribed coloring to reduce code memory requirements and optimize accessing the elemental data in memory. Th…
Deep Neural Network (DNN) applications with edge computing presents a trade-off between responsiveness and computational resources. On one hand, edge computing can provide high responsiveness deploying computational resources close to end devices, which may be prohibitive for the majority of cloud computing services. On the other hand, DNN inference requires computational power to be executed, which may not be available on edge devices, but a cloud server can provide it. To solve this problem (trade-off), we partition a DNN between edge device and cloud server, which means the first DNN layers…
Many important real-world applications-such as social networks or distributed data bases-can be modeled as hypergraphs. In such a model, vertices represent entities-such as users or data records-whereas hyperedges model a group membership of the vertices-such as the authorship in a specific topic or the membership of a data record in a specific replicated shard. To optimize such applications, we need an efficient and effective solution to the NP-hard balanced k-way hypergraph partitioning problem. However, existing hypergraph partitioners that scale to very large graphs do not effectively expl…
Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) is demonstrated to efficiently solve eigenvalue problems for graph Laplacians that appear in spectral clustering. For static graph partitioning, 10-20 iterations of LOBPCG without preconditioning result in ~10x error reduction, enough to achieve 100% correctness for all Challenge datasets with known truth partitions, e.g., for graphs with 5K/.1M (50K/1M) Vertices/Edges in 2 (7) seconds, compared to over 5,000 (30,000) seconds needed by the baseline Python code. Our Python code 100% correctly determines 98 (160) clusters from the …
The dynamic scaling of distributed computations plays an important role in the utilization of elastic computational resources, such as the cloud. It enables the provisioning and de-provisioning of resources to match dynamic resource availability and demands. In the case of distributed graph processing, changing the number of the graph partitions while maintaining high partitioning quality imposes serious computational overheads as typically a time-consuming graph partitioning algorithm needs to execute each time repartitioning is required. In this paper, we propose a dynamic scaling method tha…
This paper severs as a user guide to the graph partitioning framework KaHIP (Karlsruhe High Quality Partitioning). We give a rough overview of the techniques used within the framework and describe the user interface as well as the file formats used. Moreover, we provide a short description of the current library functions provided within the framework. Since version 3.00 we support multilevel partitioning, memetic algorithms, distributed and shared-memory parallel algorithms, node separator and ordering algorithms, edge partitioning algorithms as well as ILP solvers.
Mobile Edge Computing (MEC) has emerged as a promising supporting architecture providing a variety of resources to the network edge, thus acting as an enabler for edge intelligence services empowering massive mobile and Internet of Things (IoT) devices with AI capability. With the assistance of edge servers, user equipments (UEs) are able to run deep neural network (DNN) based AI applications, which are generally resource-hungry and compute-intensive, such that an individual UE can hardly afford by itself in real time. However the resources in each individual edge server are typically limited.…
Balanced graph partitioning is a critical step for many large-scale distributed computations with relational data. As graph datasets have grown in size and density, a range of highly-scalable balanced partitioning algorithms have appeared to meet varied demands across different domains. As the starting point for the present work, we observe that two recently introduced families of iterative partitioners---those based on restreaming and those based on balanced label propagation (including Facebook's Social Hash Partitioner)---can be viewed through a common modular framework of design decisions.…
Sun Yat-sen University（中山大学）；University of Nevada, Reno（内华达大学里诺分校）；Arizona State University（亚利桑那州立大学）
Recent advances in artificial intelligence have driven increasing intelligent applications at the network edge, such as smart home, smart factory, and smart city. To deploy computationally intensive Deep Neural Networks (DNNs) on resource-constrained edge devices, traditional approaches have relied on either offloading workload to the remote cloud or optimizing computation at the end device locally. However, the cloud-assisted approaches suffer from the unreliable and delay-significant wide-area network, and the local computing approaches are limited by the constrained computing capability. To…
Large-scale knowledge graphs are increasingly common in many domains. Their large sizes often exceed the limits of systems storing the graphs in a centralized data store, especially if placed in main memory. To overcome this, large knowledge graphs need to be partitioned into multiple sub-graphs and placed in nodes in a distributed system. But querying these fragmented sub-graphs poses new challenges, such as increased communication costs, due to distributed joins involving cut edges. To combat these problems, a good partitioning should reduce the edge cuts while considering a given query work…
The most commonly used method to tackle the graph partitioning problem in practice is the multilevel approach. During a coarsening phase, a multilevel graph partitioning algorithm reduces the graph size by iteratively contracting nodes and edges until the graph is small enough to be partitioned by some other algorithm. A partition of the input graph is then constructed by successively transferring the solution to the next finer graph and applying a local search algorithm to improve the current solution. In this paper, we describe a novel approach to partition graphs effectively especially if t…
Carnegie Mellon University（卡内基梅隆大学）；Microsoft Research（微软研究院）；University of Pittsburgh（匹兹堡大学）；Clutterbot
Emerging Internet of Things (IoT) and mobile computing applications are expected to support latency-sensitive deep neural network (DNN) workloads. To realize this vision, the Internet is evolving towards an edge-computing architecture, where computing infrastructure is located closer to the end device to help achieve low latency. However, edge computing may have limited resources compared to cloud environments and thus, cannot run large DNN models that often have high accuracy. In this work, we develop REACT, a framework that leverages cloud resources to execute large DNN models with higher ac…
