A Multiscale Pyramid Transform for Graph Signals

Multiscale transforms designed to process analog and discrete-time signals and images cannot be directly applied to analyze high-dimensional data residing on the vertices of a weighted graph, as they do not capture the intrinsic geometric structure of the underlying graph data domain. In this paper, we adapt the Laplacian pyramid transform for signals on Euclidean domains so that it can be used to analyze high-dimensional data residing on the vertices of a weighted graph. Our approach is to study existing methods and develop new methods for the four fundamental operations of graph downsampling, graph reduction, and filtering and interpolation of signals on graphs. Equipped with appropriate notions of these operations, we leverage the basic multiscale constructs and intuitions from classical signal processing to generate a transform that yields both a multiresolution of graphs and an associated multiresolution of a graph signal on the underlying sequence of graphs.Comment: 16 pages, 13 figure

A Network Resource Allocation Recommendation Method with An Improved Similarity Measure

Recommender systems have been acknowledged as efficacious tools for managing information overload. Nevertheless, conventional algorithms adopted in such systems primarily emphasize precise recommendations and, consequently, overlook other vital aspects like the coverage, diversity, and novelty of items. This approach results in less exposure for long-tail items. In this paper, to personalize the recommendations and allocate recommendation resources more purposively, a method named PIM+RA is proposed. This method utilizes a bipartite network that incorporates self-connecting edges and weights. Furthermore, an improved Pearson correlation coefficient is employed for better redistribution. The evaluation of PIM+RA demonstrates a significant enhancement not only in accuracy but also in coverage, diversity, and novelty of the recommendation. It leads to a better balance in recommendation frequency by providing effective exposure to long-tail items, while allowing customized parameters to adjust the recommendation list bias

Locally Optimal Load Balancing

This work studies distributed algorithms for locally optimal load-balancing: We are given a graph of maximum degree $\Delta$, and each node has up to $L$ units of load. The task is to distribute the load more evenly so that the loads of adjacent nodes differ by at most $1$. If the graph is a path ($\Delta = 2$), it is easy to solve the fractional version of the problem in $O(L)$ communication rounds, independently of the number of nodes. We show that this is tight, and we show that it is possible to solve also the discrete version of the problem in $O(L)$ rounds in paths. For the general case ($\Delta > 2$), we show that fractional load balancing can be solved in $\operatorname{poly}(L,\Delta)$ rounds and discrete load balancing in $f(L,\Delta)$ rounds for some function $f$, independently of the number of nodes.Comment: 19 pages, 11 figure