Natural graphs, such as social networks, email graphs, or instant messaging patterns, have become pervasive through the internet. These graphs are massive, often containing hundreds of millions of nodes and billions of edges. While some theoretical models have been proposed to study such graphs, their analysis is still difficult due to the scale and nature of the data. We propose a framework for large-scale graph decomposition and inference. To resolve the scale, our framework is distributed so that the data are partitioned over a sharednothing set of machines. We propose a novel factorization technique that relies on partitioning a graph so as to minimize the number of neighboring vertices rather than edges across partitions. Our decomposition is based on a streaming algorithm. It is network-aware as it adapts to the network topology of the underlying computational hardware. We use local copies of the variables and an efficient asynchronous communication protocol to synchronize the replicated values in order to perform most of the computation without having to incur the cost of network communication. On a graph of 200 million vertices and 10 billion edges, derived from an email communication network, our algorithm retains convergence properties while allowing for almost linear scalability in the number of computers.

This paper describes a high performance sampling architecture for inference of latent topic models on a cluster of workstations. Our system is faster than previous work by over an order of magnitude and it is capable of dealing with hundreds of millions of documents and thousands of topics.The algorithm relies on a novel communication structure, namely the use of a distributed (key, value) storage for synchronizing the sampler state between computers. Our architecture entirely obviates the need for separate computation and synchronization phases. Instead, disk, CPU, and network are used simultaneously to achieve high performance. We show that this architecture is entirely general and that it can be extended easily to more sophisticated latent variable models such as n-grams and hierarchies.

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Increasingly, organizations capture, transform and analyze enormous data sets. Prominent examples include internet companies and e-science. The Map-Reduce scalable dataflow paradigm has become popular for these applications. Its simple, explicit dataflow programming model is favored by some over the traditional high-level declarative approach: SQL. On the other hand, the extreme simplicity of Map-Reduce leads to much low-level hacking to deal with the many-step, branching dataflows that arise in practice. Moreover, users must repeatedly code standard operations such as join by hand. These practices waste time, introduce bugs, harm readability, and impede optimizations. Pig is a high-level dataflow system that aims at a sweet spot between SQL and Map-Reduce. Pig offers SQL-style high-level data manipulation constructs, which can be assembled in an explicit dataflow and interleaved with custom Map-and Reduce-style functions or executables. Pig programs are compiled into sequences of Map-Reduce jobs, and executed in the Hadoop Map-Reduce environment. Both Pig and Hadoop are open-source projects administered by the Apache Software Foundation. This paper describes the challenges we faced in developing Pig, and reports performance comparisons between Pig execution and raw Map-Reduce execution.

In this work we address the question of finding symmetries of a given MDP. We show that the problem is Isomorphism Complete, that is, the problem is polynomially equivalent to verifying whether two graphs are isomorphic. Apart from the theoretical importance of this result it has an important practical application. The reduction presented can be used together with any off-the-shelf Graph Isomorphism solver, which performs well in the average case, to find symmetries of an MDP. In fact, we present results of using NAutY (the best Graph Isomorphism solver currently available), to find symmetries of MDPs.