Let k be a positive integer and G a bipartite graph with bipartition (X,Y). A perfect 1-k matching is an edge subset M of G such that each vertex in Y is incident with exactly one edge in M and each vertex in X is inc...Let k be a positive integer and G a bipartite graph with bipartition (X,Y). A perfect 1-k matching is an edge subset M of G such that each vertex in Y is incident with exactly one edge in M and each vertex in X is incident with exactly k edges in M. A perfect 1-k matching is an optimal semi-matching related to the load-balancing problem, where a semi-matching is an edge subset M such that each vertex in Y is incident with exactly one edge in M, and a vertex in X can be incident with an arbitrary number of edges in M. In this paper, we give three sufficient and necessary conditions for the existence of perfect 1-k matchings and for the existence of 1-k matchings covering | X |−dvertices in X, respectively, and characterize k-elementary bipartite graph which is a graph such that the subgraph induced by all k-allowed edges is connected, where an edge is k-allowed if it is contained in a perfect 1-k matching.展开更多
针对现有的M通道过采样图滤波器组整体性能较差的问题,该文提出一种过采样图滤波器组设计的新算法。在新算法中,分两步来设计图滤波器组。首先,从频谱特性方面考虑来设计分析滤波器,以分析滤波器的通带波纹和阻带能量为目标函数,以3 d ...针对现有的M通道过采样图滤波器组整体性能较差的问题,该文提出一种过采样图滤波器组设计的新算法。在新算法中,分两步来设计图滤波器组。首先,从频谱特性方面考虑来设计分析滤波器,以分析滤波器的通带波纹和阻带能量为目标函数,以3 d B约束为约束条件,通过半正定规划求解出频谱选择性较好的分析滤波器;然后,从完全重构特性方面考虑来设计综合滤波器,以综合滤波器的阻带能量为目标函数,以完全重构条件为约束函数。上述两个约束优化问题都是半正定规划问题,都可有效地求解。新算法综合考虑了滤波器组的重构特性和频率特性,因此可以设计得到整体性能良好的M通道双正交过采样的图滤波器组。仿真对比表明,与已有的设计算法相比,新算法设计所得的图滤波器组具备更小的重构误差。展开更多
文摘Let k be a positive integer and G a bipartite graph with bipartition (X,Y). A perfect 1-k matching is an edge subset M of G such that each vertex in Y is incident with exactly one edge in M and each vertex in X is incident with exactly k edges in M. A perfect 1-k matching is an optimal semi-matching related to the load-balancing problem, where a semi-matching is an edge subset M such that each vertex in Y is incident with exactly one edge in M, and a vertex in X can be incident with an arbitrary number of edges in M. In this paper, we give three sufficient and necessary conditions for the existence of perfect 1-k matchings and for the existence of 1-k matchings covering | X |−dvertices in X, respectively, and characterize k-elementary bipartite graph which is a graph such that the subgraph induced by all k-allowed edges is connected, where an edge is k-allowed if it is contained in a perfect 1-k matching.
文摘针对现有的M通道过采样图滤波器组整体性能较差的问题,该文提出一种过采样图滤波器组设计的新算法。在新算法中,分两步来设计图滤波器组。首先,从频谱特性方面考虑来设计分析滤波器,以分析滤波器的通带波纹和阻带能量为目标函数,以3 d B约束为约束条件,通过半正定规划求解出频谱选择性较好的分析滤波器;然后,从完全重构特性方面考虑来设计综合滤波器,以综合滤波器的阻带能量为目标函数,以完全重构条件为约束函数。上述两个约束优化问题都是半正定规划问题,都可有效地求解。新算法综合考虑了滤波器组的重构特性和频率特性,因此可以设计得到整体性能良好的M通道双正交过采样的图滤波器组。仿真对比表明,与已有的设计算法相比,新算法设计所得的图滤波器组具备更小的重构误差。
