The neighbourhood function N(t) of a graph G gives, for each t, the number of pairs of nodes such that y is reachable from x in less that t hops. The neighbourhood function provides a wealth of information about the graph (e.g., it easily allows one to compute its diameter), but it is very expensive to compute it exactly. Recently, the ANF algorithm (approximate neighbourhood function) has been proposed with the purpose of approximating NG(t) on large graphs. We describe a breakthrough improvement over ANF in terms of speed and scalability. Our algorithm, called HyperANF, uses the new HyperLogLog counters and combines them efficiently through broadword programming; our implementation uses overdecomposition to exploit multi-core parallelism. With HyperANF, for the first time we can compute in a few hours the neighbourhood function of graphs with billions of nodes with a small error and good confidence using a standard workstation. Then, we turn to the study of the distribution of the shortest paths between reachable nodes (that can be efficiently approximated by means of HyperANF), and discover the surprising fact that its index of dispersion provides a clear-cut characterisation of proper social networks vs. web graphs. We thus propose the spid (Shortest-Paths Index of Dispersion) of a graph as a new, informative statistics that is able to discriminate between the above two types of graphs. We believe this is the first proposal of a significant new non-local structural index for complex networks whose computation is highly scalable.
Recently, a MapReduce-based distributed implementation of ANF called HADI @cite_7 has been presented. HADI runs on one of the fifty largest supercomputers---the Hadoop cluster M45. The only published data about HADI's performance is the computation of the neighbourhood function of a Kronecker graph with 2 billion links, which required half an hour using 90 machines. HyperANF can compute the same function in .
@cite_7
1569778844 2010279913 2581614494 2067005380
We present VC3, the first system that allows users to run distributed MapReduce computations in the cloud while keeping their code and data secret, and ensuring the correctness and completeness of their results. VC3 runs on unmodified Hadoop, but crucially keeps Hadoop, the operating system and the hyper visor out of the TCB, thus, confidentiality and integrity are preserved even if these large components are compromised. VC3 relies on SGX processors to isolate memory regions on individual computers, and to deploy new protocols that secure distributed MapReduce computations. VC3 optionally enforces region self-integrity invariants for all MapReduce code running within isolated regions, to prevent attacks due to unsafe memory reads and writes. Experimental results on common benchmarks show that VC3 performs well compared with unprotected Hadoop: VC3's average runtime overhead is negligible for its base security guarantees, 4.5 with write integrity and 8 with read write integrity. MapReduce has been widely used for large-scale data analysis in the Cloud. The system is well recognized for its elastic scalability and fine-grained fault tolerance although its performance has been noted to be suboptimal in the database context. According to a recent study [19], Hadoop, an open source implementation of MapReduce, is slower than two state-of-the-art parallel database systems in performing a variety of analytical tasks by a factor of 3.1 to 6.5. MapReduce can achieve better performance with the allocation of more compute nodes from the cloud to speed up computation; however, this approach of "renting more nodes" is not cost effective in a pay-as-you-go environment. Users desire an economical elastically scalable data processing system, and therefore, are interested in whether MapReduce can offer both elastic scalability and efficiency. In this paper, we conduct a performance study of MapReduce (Hadoop) on a 100-node cluster of Amazon EC2 with various levels of parallelism. We identify five design factors that affect the performance of Hadoop, and investigate alternative but known methods for each factor. We show that by carefully tuning these factors, the overall performance of Hadoop can be improved by a factor of 2.5 to 3.5 for the same benchmark used in [19], and is thus more comparable to that of parallel database systems. Our results show that it is therefore possible to build a cloud data processing system that is both elastically scalable and efficient. Nowadays MapReduce and its open source implementation, Apache Hadoop, are the most widespread solutions for handling massive dataset on clusters of commodity hardware. At the expense of a somewhat reduced performance in comparison to HPC technologies, the MapReduce framework provides fault tolerance and automatic parallelization without any efforts by developers. Since in many cases Hadoop is adopted to support business critical activities, it is often important to predict with fair confidence the execution time of submitted jobs, for instance when SLAs are established with end-users. In this work, we propose and validate a hybrid approach exploiting both queuing networks and support vector regression, in order to achieve a good accuracy without too many costly experiments on a real setup. The experimental results show how the proposed approach attains a 21 improvement in accuracy over applying machine learning techniques without any support from analytical models. MapReduce is becoming the state-of-the-art computing paradigm for processing large-scale datasets on a large cluster with tens or thousands of nodes. It has been widely used in various fields such as e-commerce, Web search, social networks, and scientific computation. Understanding the characteristics of MapReduce workloads is the key to achieving better configuration decisions and improving the system throughput. However, workload characterization of MapReduce, especially in a large-scale production environment, has not been well studied yet. To gain insight on MapReduce workloads, we collected a two-week workload trace from a 2,000-node Hadoop cluster at Taobao, which is the biggest online e-commerce enterprise in Asia, ranked 14th in the world as reported by Alexa. The workload trace covered 912,157 jobs, logged from Dec. 4 to Dec. 20, 2011. We characterized the workload at the granularity of job and task, respectively and concluded with a set of interesting observations. The results of workload characterization are representative and generally consistent with data platforms for e-commerce websites, which can help other researchers and engineers understand the performance and job characteristics of Hadoop in their production environments. In addition, we use these job analysis statistics to derive several implications for potential performance optimization solutions.