Some reverses of the continuous triangle inequality for Bochner integral of vectorvalued functions in Hilbert spaces are given. Applications for complex-valued functions are provided as well.

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Clustering divides data objects into groups to minimize the variation within each group. This technique is widely used in data mining and other areas of computer science. K-means is a partitional clustering algorithm that produces a fixed number of clusters through an iterative process. The relative simplicity and obvious data parallelism of the K-means algorithm make it an excellent candidate ...

The geodesic distance (path length) and effective resistance are both metrics defined on the vertices of a graph. The effective resistance is a more refined measure of connectivity than the geodesic distance. For example if there are k edge disjoint paths of geodesic distance d between two vertices, then the effective resistance is no more than d k . Thus, the more paths, the closer the vertice...

This article deals with a bi-objective matching problem. The input is a complete graph and two values on each edge (a weight and a length) which satisfy the triangle inequality. It is unlikely that every instance admits a matching with maximum weight and maximum length at the same time. Therefore, we look for a compromise solution, i.e. a matching that simultaneously approximates the best weigh...