Todd D. Plantenga

On the Implementation of an Algorithm for Large-Scale Equality Constrained Optimization

This paper describes a software implementation of Byrd and Omojokuns trust region algorithm for solving nonlinear equality constrained optimization problems. The code is designed for the efficient solution of large problems and provides the user with a variety of linear algebra techniques for solving the subproblems occurring in the algorithm. Second derivative information can be used, but when it is not available, limited memory quasi-Newton approximations are made. The performance of the code is studied using a set of difficult test problems from the CUTE collection.

A Scalable Generative Graph Model with Community Structure

Network data is ubiquitous and growing, yet we lack realistic generative network models that can be calibrated to match real-world data. The recently proposed block two-level Erdos--Renyi (BTER) model can be tuned to capture two fundamental properties: degree distribution and clustering coefficients. The latter is particularly important for reproducing graphs with community structure, such as social networks. In this paper, we compare BTER to other scalable models and show that it gives a better fit to real data. We provide a scalable implementation that requires only

Counting Triangles in Massive Graphs with MapReduce

O(d_{\rm max})

Inexact subgraph isomorphism in MapReduce

storage, where

Efficiently Computing Tensor Eigenvalues on a GPU

d_{\rm max}

A Trust Region Method for Nonlinear Programming Based on Primal Interior-Point Techniques

is the maximum number of neighbors for a single node. The generator is trivially parallelizable, and we show results for a Hadoop MapReduce implementation for modeling a real-world Web graph with over 4.6 billion edges. We propose that the BTER model can be used as a graph generator for benchmarking purposes and provide idealized degree distributions and clustering coefficient profiles that can b...

Newton-based optimization for Kullback–Leibler nonnegative tensor factorizations

Graphs and networks are used to model interactions in a variety of contexts. There is a growing need to quickly assess the characteristics of a graph in order to understand its underlying structure. Some of the most useful metrics are triangle-based and give a measure of the connectedness of mutual friends. This is often summarized in terms of clustering coefficients, which measure the likelihood that two neighbors of a node are themselves connected. Computing these measures exactly for large-scale networks is prohibitively expensive in both memory and time. However, a recent wedge-sampling algorithm has proved successful in efficiently and accurately estimating clustering coefficients. In this paper, we describe how to implement this approach in MapReduce to deal with massive graphs. We show results on publicly available networks, the largest of which is 132M nodes and 4.7B edges, as well as artificially generated networks (using the Graph500 benchmark), the largest of which has 240M nodes and 8.5B edges...

Using Performance Measurements to Improve MapReduce Algorithms

Inexact subgraph matching based on type-isomorphism was introduced by Berry et al. [J. Berry, B. Hendrickson, S. Kahan, P. Konecny, Software and algorithms for graph queries on multithreaded architectures, in: Proc. IEEE International Parallel and Distributed Computing Symposium, IEEE, 2007, pp. 1-14] as a generalization of the exact subgraph matching problem. Enumerating small subgraph patterns in very large graphs is a core problem in the analysis of social networks, bioinformatics data sets, and other applications. This paper describes a MapReduce algorithm for subgraph type-isomorphism matching. The MapReduce computing framework is designed for distributed computing on massive data sets, and the new algorithm leverages MapReduce techniques to enable processing of graphs with billions of vertices. The paper also introduces a new class of walk-level constraints for narrowing the set of matches. Constraints meeting criteria defined in the paper are useful for specifying more precise patterns and for improving algorithm performance. Results are provided on a variety of graphs, with size ranging up to billions of vertices and edges, including graphs that follow a power law degree distribution.

C%2B%2B tensor toolbox user manual.

The tensor eigenproblem has many important applications, generating both mathematical and application-specific interest in the properties of tensor eigenpairs and methods for computing them. A tensor is an

Simulation templates in the SUMMIT system.

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