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The R-MAT graph generator introduced by Chakrabarti, Faloutsos, and Zhan [6] offers a simple, fast method for generating very large directed graphs. These properties have made it a popular choice as a method of generating graphs for objects of study in a variety of disciplines, from social network analysis to high performance computing. We analyze the… (More)

Let G be a finite simple directed graph on n vertices. Say G is m-free if it has no directed cycles of length at most m. In 1978, Caccetta and Häggkvist [3] conjectured that if G has minimum out-degree at least r, then G is not n/r-free. Finding upper bounds on the minimum out-degree in 3-free digraphs has been of particular interest in recent research. In… (More)

We describe using OpenMP to compute δ-hyperbolicity, a quantity of interest in social and information network analysis, at a scale that uses up to 1000 threads. By considering both OpenMP workshare and tasking models to parallelize the computations, we find that multiple task levels permits finer grained tasks at runtime and results in better performance at… (More)

Although large social and information networks are often thought of as having hierarchical or tree-like structure, this assumption is rarely tested. We have performed a detailed empirical analysis of the tree-like properties of realistic informatics graphs using two very different notions of tree-likeness: Gromov's d-hyperbolicity, which is a notion from… (More)

Graphs are a powerful way to model interactions and relationships in data from a wide variety of application domains. In this setting, entities represented by vertices at the 'center' of the graph are often more important than those associated with vertices on the 'fringes'. For example, central nodes tend to be more critical in the spread of information or… (More)

Let Fp = Z/pZ. The height of a point a = (a 1 ,. .. , a d) ∈ F d p is hp(a) = min n P d i=1 (ka i mod p) : k = 1,. .. , p − 1 o. Explicit formulas and estimates are obtained for the values of the height function in the case d = 2, and these results are applied to the problem of determining the minimum number of edges the must be deleted from a finite… (More)

Reports produced before January 1, 1996, may be purchased by members of the public from the following source: This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal… (More)

Although many NP-hard graph optimization problems can be solved in polynomial time on graphs of bounded tree-width, the adoption of these techniques into mainstream scientific computation has been limited due to the high memory requirements of the dynamic programming tables and excessive runtimes of sequential implementations. This work addresses both… (More)