In this paper we propose to generalize Jaccard and related measures, often used as similarity coefficients between two sets. We define Jaccard, Dice-Sorensen and Tversky edge weights on a graph and generalize them to account for vertex weights. We develop an efficient parallel algorithm for computing Jaccard edge and PageRank vertex weights. We highlight that the weights computation can obtain more than 10× speedup on the GPU versus CPU on large realistic data sets. Also, we show that finding a minimum balanced cut for modified weights can be related to minimizing the sum of ratios of the intersection and union of nodes on the boundary of clusters. Finally, we show that the novel weights can improve the quality of the graph clustering by about 15% and 80% for multi-level and spectral graph partitioning and clustering schemes, respectively.
In this paper we present a parallel strategy for solving Eikonal and related static (steady state) Hamilton-Jacobi equations using the Fast Iterative Method. The Fast Iterative Method is a variant of the Fast Marching Method which is more fitted for parallel computing since it is basically designed for graphic processing units (GPUs). We propose a parallel model based on front partitioning which particularly fits shared-memory architectures. We review Fast Marching Method parallel methods, we explain our parallel strategy and give a performance analysis.
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