We propose a new numerical algorithm for computing the tensor rank decomposition or canonical polyadic of higher-order tensors subject to and genericity constraint. Reformulating this computational problem as system polynomial equations allows us leverage recent linear algebra tools from algebraic geometry. characterize complexity our in terms an property system—the multigraded regularity. prov...

The notion of H-matroids was introduced by U. Faigle and S. Fujishige in 2009 as a general model for matroids and the greedy algorithm. They gave a characterization of H-matroids by the greedy algorithm. In this note, we give a characterization of some H-matroids by rank functions. 2010 MSC: 05B35, 90C27

We provide a framework for online conflict-free coloring (CF-coloring) of any hypergraph. We use this framework to obtain an efficient randomized online algorithm for CF-coloring any k-degenerate hypergraph. Our algorithm uses O(k log n) colors with high probability and this bound is asymptotically optimal for any constant k. Moreover, our algorithm uses O(k log k log n) random bits with high p...

Collaborative filtering (CF) has proved to be one of the most effective information filtering techniques. However, as their calculation complexity increased quickly both in time and space when the record in user database increases, traditional centralized CF algorithms has suffered from their shortage in scalability. In this paper, we first propose a novel distributed CF algorithm called PipeCF...

Collaborative filtering (CF) recommendation is a knowledge sharing technology for distribution of opinions and facilitating contacts in network society between people with similar interests. The main concerns of the CF algorithm are about prediction accuracy, speed of response time, problem of data sparsity, and scalability. In general, the efforts of improving prediction algorithms and lesseni...