For a given graph G, a k-role assignment of G is a surjective function ?such that , where N(x) and N(y) are the neighborhoods of x and y, respectively. Furthermore, as we limit the number of different roles in the nei...For a given graph G, a k-role assignment of G is a surjective function ?such that , where N(x) and N(y) are the neighborhoods of x and y, respectively. Furthermore, as we limit the number of different roles in the neighborhood of an individual, we call r a restricted size k-role assignment. When the hausdorff distance between the sets of roles assigned to their neighbors is at most 1, we call r a k-threshold close role assignment. In this paper we study the graphs that have k-role assignments, restricted size k-role assignments and k-threshold close role assignments, respectively. By the end we discuss the maximal and minimal graphs which have k-role assignments.展开更多
Sparse signals can be possibly reconstructed by an algorithm which merges a traditional nonlinear optimization method and a certain thresholding technique.Different from existing thresholding methods,a novel threshold...Sparse signals can be possibly reconstructed by an algorithm which merges a traditional nonlinear optimization method and a certain thresholding technique.Different from existing thresholding methods,a novel thresholding technique referred to as the optimal k-thresholding was recently proposed by Zhao(SIAM J Optim 30(1):31-55,2020).This technique simultaneously performs the minimization of an error metric for the problem and thresholding of the iterates generated by the classic gradient method.In this paper,we propose the so-called Newton-type optimal k-thresholding(NTOT)algorithm which is motivated by the appreciable performance of both Newton-type methods and the optimal k-thresholding technique for signal recovery.The guaranteed performance(including convergence)of the proposed algorithms is shown in terms of suitable choices of the algorithmic parameters and the restricted isometry property(RIP)of the sensing matrix which has been widely used in the analysis of compressive sensing algorithms.The simulation results based on synthetic signals indicate that the proposed algorithms are stable and efficient for signal recovery.展开更多
文摘For a given graph G, a k-role assignment of G is a surjective function ?such that , where N(x) and N(y) are the neighborhoods of x and y, respectively. Furthermore, as we limit the number of different roles in the neighborhood of an individual, we call r a restricted size k-role assignment. When the hausdorff distance between the sets of roles assigned to their neighbors is at most 1, we call r a k-threshold close role assignment. In this paper we study the graphs that have k-role assignments, restricted size k-role assignments and k-threshold close role assignments, respectively. By the end we discuss the maximal and minimal graphs which have k-role assignments.
基金founded by the National Natural Science Foundation of China(No.12071307).
文摘Sparse signals can be possibly reconstructed by an algorithm which merges a traditional nonlinear optimization method and a certain thresholding technique.Different from existing thresholding methods,a novel thresholding technique referred to as the optimal k-thresholding was recently proposed by Zhao(SIAM J Optim 30(1):31-55,2020).This technique simultaneously performs the minimization of an error metric for the problem and thresholding of the iterates generated by the classic gradient method.In this paper,we propose the so-called Newton-type optimal k-thresholding(NTOT)algorithm which is motivated by the appreciable performance of both Newton-type methods and the optimal k-thresholding technique for signal recovery.The guaranteed performance(including convergence)of the proposed algorithms is shown in terms of suitable choices of the algorithmic parameters and the restricted isometry property(RIP)of the sensing matrix which has been widely used in the analysis of compressive sensing algorithms.The simulation results based on synthetic signals indicate that the proposed algorithms are stable and efficient for signal recovery.
