87,955 research outputs found
Extremal Lipschitz functions in the deviation inequalities from the mean
We obtain an optimal deviation from the mean upper bound \begin{equation}
D(x)\=\sup_{f\in \F}\mu\{f-\E_{\mu} f\geq x\},\qquad\ \text{for}\
x\in\R\label{abstr} \end{equation} where \F is the class of the integrable,
Lipschitz functions on probability metric (product) spaces. As corollaries we
get exact solutions of \eqref{abstr} for Euclidean unit sphere with
a geodesic distance and a normalized Haar measure, for equipped with a
Gaussian measure and for the multidimensional cube, rectangle, torus or Diamond
graph equipped with uniform measure and Hamming distance. We also prove that in
general probability metric spaces the in \eqref{abstr} is achieved on
a family of distance functions.Comment: 7 page
On the algorithmic complexity of twelve covering and independence parameters of graphs
The definitions of four previously studied parameters related to total coverings and total matchings of graphs can be restricted, thereby obtaining eight parameters related to covering and independence, each of which has been studied previously in some form. Here we survey briefly results concerning total coverings and total matchings of graphs, and consider the aforementioned 12 covering and independence parameters with regard to algorithmic complexity. We survey briefly known results for several graph classes, and obtain new NP-completeness results for the minimum total cover and maximum minimal total cover problems in planar graphs, the minimum maximal total matching problem in bipartite and chordal graphs, and the minimum independent dominating set problem in planar cubic graphs
Multiangle social network recommendation algorithms and similarity network evaluation
Multiangle social network recommendation algorithms (MSN) and a new assessmentmethod, called similarity network evaluation (SNE), are both proposed. From the viewpoint of six dimensions, the MSN are classified into six algorithms, including user-based algorithmfromresource point (UBR), user-based algorithmfromtag point (UBT), resource-based algorithm fromtag point (RBT), resource-based algorithm from user point (RBU), tag-based algorithm from resource point (TBR), and tag-based algorithm from user point (TBU). Compared with the traditional recall/precision (RP) method, the SNE is more simple, effective, and visualized. The simulation results show that TBR and UBR are the best algorithms, RBU and TBU are the worst ones, and UBT and RBT are in the medium levels
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