Blair D. Sullivan

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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 Fp = Z/pZ. The height of a point a = (a1, . . . , ad) ∈ F d p is hp(a) = min n Pd i=1(kai 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)
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 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 dn/re-free. Finding upper bounds on the minimum out-degree in 3-free digraphs has been of particular interest in recent research.(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)
We study the computational complexity of the graph modification problems Threshold Editing and Chain Editing, adding and deleting as few edges as possible to transform the input into a threshold (or chain) graph. In this article, we show that both problems are NP-hard, resolving a conjecture by Natanzon, Shamir, and Sharan (Discrete Applied Mathematics,(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)