2 research outputs found

    Parallel and External High Quality Graph Partitioning

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    Partitioning graphs into k blocks of roughly equal size such that few edges run between the blocks is a key tool for processing and analyzing large complex real-world networks. The graph partitioning problem has multiple practical applications in parallel and distributed computations, data storage, image processing, VLSI physical design and many more. Furthermore, recently, size, variety, and structural complexity of real-world networks has grown dramatically. Therefore, there is a demand for efficient graph partitioning algorithms that fully utilize computational power and memory capacity of modern machines. A popular and successful heuristic to compute a high-quality partitions of large networks in reasonable time is multi-level graph partitioning\textit{multi-level graph partitioning} approach which contracts the graph preserving its structure and then partitions it using a complex graph partitioning algorithm. Specifically, the multi-level graph partitioning approach consists of three main phases: coarsening, initial partitioning, and uncoarsening. During the coarsening phase, the graph is recursively contracted preserving its structure and properties until it is small enough to compute its initial partition during the initial partitioning phase. Afterwards, during the uncoarsening phase the partition of the contracted graph is projected onto the original graph and refined using, for example, local search. Most of the research on heuristical graph partitioning focuses on sequential algorithms or parallel algorithms in the distributed memory model. Unfortunately, previous approaches to graph partitioning are not able to process large networks and rarely take in into account several aspects of modern computational machines. Specifically, the amount of cores per chip grows each year as well as the price of RAM reduces slower than the real-world graphs grow. Since HDDs and SSDs are 50 – 400 times cheaper than RAM, external memory makes it possible to process large real-world graphs for a reasonable price. Therefore, in order to better utilize contemporary computational machines, we develop efficient multi-level graph partitioning\textit{multi-level graph partitioning} algorithms for the shared-memory and the external memory models. First, we present an approach to shared-memory parallel multi-level graph partitioning that guarantees balanced solutions, shows high speed-ups for a variety of large graphs and yields very good quality independently of the number of cores used. Important ingredients include parallel label propagation for both coarsening and uncoarsening, parallel initial partitioning, a simple yet effective approach to parallel localized local search, and fast locality preserving hash tables that effectively utilizes caches. The main idea of the parallel localized local search is that each processors refines only a small area around a random vertex reducing interactions between processors. For example, on 79 cores, our algorithms partitions a graph with more than 3 billions of edges into 16 blocks cutting 4.5% less edges than the closest competitor and being more than two times faster. Furthermore, another competitors is not able to partition this graph. We then present an approach to external memory graph partitioning that is able to partition large graphs that do not fit into RAM. Specifically, we consider the semi-external and the external memory model. In both models a data structure of size proportional to the number of edges does not fit into the RAM. The difference is that the former model assumes that a data structure of size proportional to the number of vertices fits into the RAM whereas the latter assumes the opposite. We address the graph partitioning problem in both models by adapting the size-constrained label propagation technique for the semi-external model and by developing a size-constrained clustering algorithm based on graph coloring in the external memory. Our semi-external size-constrained label propagation algorithm (or external memory clustering algorithm) can be used to compute graph clusterings and is a prerequisite for the (semi-)external graph partitioning algorithm. The algorithms are then used for both the coarsening and the uncoarsening phase of a multi-level algorithm to compute graph partitions. Our (semi-)external algorithm is able to partition and cluster huge complex networks with billions of edges on cheap commodity machines. Experiments demonstrate that the semi-external graph partitioning algorithm is scalable and can compute high quality partitions in time that is comparable to the running time of an efficient internal memory implementation. A parallelization of the algorithm in the semi-external model further reduces running times. Additionally, we develop a speed-up technique for the hypergraph partitioning algorithms. Hypergraphs are an extension of graphs that allow a single edge to connect more than two vertices. Therefore, they describe models and processes more accurately additionally allowing more possibilities for improvement. Most multi-level hypergraph partitioning algorithms perform some computations on vertices and their set of neighbors. Since these computations can be super-linear, they have a significant impact on the overall running time on large hypergraphs. Therefore, to further reduce the size of hyperedges, we develop a pin-sparsifier based on the min-hash technique that clusters vertices with similar neighborhood. Further, vertices that belong to the same cluster are substituted by one vertex, which is connected to their neighbors, therefore, reducing the size of the hypergraph. Our algorithm sparsifies a hypergraph such that the resulting graph can be partitioned significantly faster without loss in quality (or with insignificant loss). On average, KaHyPar with sparsifier performs partitioning about 1.5 times faster while preserving solution quality if hyperedges are large. All aforementioned frameworks are publicly available

    A job response time prediction method for production Grid computing environments

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    A major obstacle to the widespread adoption of Grid Computing in both the scientific community and industry sector is the difficulty of knowing in advance a job submission running cost that can be used to plan a correct allocation of resources. Traditional distributed computing solutions take advantage of homogeneous and open environments to propose prediction methods that use a detailed analysis of the hardware and software components. However, production Grid computing environments, which are large and use a complex and dynamic set of resources, present a different challenge. In Grid computing the source code of applications, programme libraries, and third-party software are not always available. In addition, Grid security policies may not agree to run hardware or software analysis tools to generate Grid components models. The objective of this research is the prediction of a job response time in production Grid computing environments. The solution is inspired by the concept of predicting future Grid behaviours based on previous experiences learned from heterogeneous Grid workload trace data. The research objective was selected with the aim of improving the Grid resource usability and the administration of Grid environments. The predicted data can be used to allocate resources in advance and inform forecasted finishing time and running costs before submission. The proposed Grid Computing Response Time Prediction (GRTP) method implements several internal stages where the workload traces are mined to produce a response time prediction for a given job. In addition, the GRTP method assesses the predicted result against the actual target job’s response time to inference information that is used to tune the methods setting parameters. The GRTP method was implemented and tested using a cross-validation technique to assess how the proposed solution generalises to independent data sets. The training set was taken from the Grid environment DAS (Distributed ASCI Supercomputer). The two testing sets were taken from AuverGrid and Grid5000 Grid environments Three consecutive tests assuming stable jobs, unstable jobs, and using a job type method to select the most appropriate prediction function were carried out. The tests offered a significant increase in prediction performance for data mining based methods applied in Grid computing environments. For instance, in Grid5000 the GRTP method answered 77 percent of job prediction requests with an error of less than 10 percent. While in the same environment, the most effective and accurate method using workload traces was only able to predict 32 percent of the cases within the same range of error. The GRTP method was able to handle unexpected changes in resources and services which affect the job response time trends and was able to adapt to new scenarios. The tests showed that the proposed GRTP method is capable of predicting job response time requests and it also improves the prediction quality when compared to other current solutions
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