Background The problem of visualizing a hierarchical dataset is an important and useful technique in many real-life situations.Folder systems,stock markets,and other hierarchical-related datasets can use this tech-niq...Background The problem of visualizing a hierarchical dataset is an important and useful technique in many real-life situations.Folder systems,stock markets,and other hierarchical-related datasets can use this tech-nique to better understand the structure and dynamic variation of the dataset.Traditional space-filling(square)-based methods have the advantages of compact space usage and node size as opposed to diagram-based methods.Space-filling-based methods have two main research directions:static and dynamic performance.Methods This study presented a treemapping method based on balanced partitioning that enables excellent aspect ratios in one variant,good temporal coherence for dynamic data in another,and in the third,a satisfactory compromise between these two aspects.To layout a treemap,all the children of a node were divided into two groups,which were then further divided until groups of single elements were reached.After this,these groups were combined to form a rectangle representing the parent node.This process was performed for each layer of the hierarchical dataset.For the first variant from the partitioning,the child elements were sorted and two groups,sized as equally as possible,were built from both big and small elements(size-balanced partition).This achieved satisfactory aspect ratios for the rec-tangles but less so temporal coherence(dynamic).For the second variant,the sequence of children was taken and from this,groups,sized as equally as possible,were created without the need for sorting(sequence-based,good compromise between aspect ratio and temporal coherency).For the third variant,the children were split into two groups of equal cardinalities,regardless of their size(number-balanced,worse aspect ratios but good temporal coherence).Results This study evaluated the aspect ratios and dynamic stability of the employed methods and proposed a new metric that measures the visual difference between rectangles during their movement to represent temporally changing inputs.Conclusion This study demonstrated that the proposed method of treemapping via balanced partitioning outperformed the state-of-the-art methods for several real-world datasets.展开更多
Because of cloud computing's high degree of polymerization calculation mode, it can't give full play to the resources of the edge device such as computing, storage, etc. Fog computing can improve the resource ...Because of cloud computing's high degree of polymerization calculation mode, it can't give full play to the resources of the edge device such as computing, storage, etc. Fog computing can improve the resource utilization efficiency of the edge device, and solve the problem about service computing of the delay-sensitive applications. This paper researches on the framework of the fog computing, and adopts Cloud Atomization Technology to turn physical nodes in different levels into virtual machine nodes. On this basis, this paper uses the graph partitioning theory to build the fog computing's load balancing algorithm based on dynamic graph partitioning. The simulation results show that the framework of the fog computing after Cloud Atomization can build the system network flexibly, and dynamic load balancing mechanism can effectively configure system resources as well as reducing the consumption of node migration brought by system changes.展开更多
Let G be a weighted hypergraph with edges of size i for i = 1, 2. Let wi denote the total weight of edges of size i and α be the maximum weight of an edge of size 1. We study the following partitioning problem of Bol...Let G be a weighted hypergraph with edges of size i for i = 1, 2. Let wi denote the total weight of edges of size i and α be the maximum weight of an edge of size 1. We study the following partitioning problem of Bollob′as and Scott： Does there exist a bipartition such that each class meets edges of total weight at least （w_1-α）/2＋（2w_2）/3？ We provide an optimal bound for balanced bipartition of weighted hypergraphs, partially establishing this conjecture. For dense graphs, we also give a result for partitions into more than two classes.In particular, it is shown that any graph G with m edges has a partition V_1,..., V_k such that each vertex set meets at least（1-（1-1/k）~2）m ＋ o（m） edges, which answers a related question of Bollobás and Scott.展开更多
文摘Background The problem of visualizing a hierarchical dataset is an important and useful technique in many real-life situations.Folder systems,stock markets,and other hierarchical-related datasets can use this tech-nique to better understand the structure and dynamic variation of the dataset.Traditional space-filling(square)-based methods have the advantages of compact space usage and node size as opposed to diagram-based methods.Space-filling-based methods have two main research directions:static and dynamic performance.Methods This study presented a treemapping method based on balanced partitioning that enables excellent aspect ratios in one variant,good temporal coherence for dynamic data in another,and in the third,a satisfactory compromise between these two aspects.To layout a treemap,all the children of a node were divided into two groups,which were then further divided until groups of single elements were reached.After this,these groups were combined to form a rectangle representing the parent node.This process was performed for each layer of the hierarchical dataset.For the first variant from the partitioning,the child elements were sorted and two groups,sized as equally as possible,were built from both big and small elements(size-balanced partition).This achieved satisfactory aspect ratios for the rec-tangles but less so temporal coherence(dynamic).For the second variant,the sequence of children was taken and from this,groups,sized as equally as possible,were created without the need for sorting(sequence-based,good compromise between aspect ratio and temporal coherency).For the third variant,the children were split into two groups of equal cardinalities,regardless of their size(number-balanced,worse aspect ratios but good temporal coherence).Results This study evaluated the aspect ratios and dynamic stability of the employed methods and proposed a new metric that measures the visual difference between rectangles during their movement to represent temporally changing inputs.Conclusion This study demonstrated that the proposed method of treemapping via balanced partitioning outperformed the state-of-the-art methods for several real-world datasets.
基金supported in part by the National Science and technology support program of P.R.China(No.2014BAH29F05)
文摘Because of cloud computing's high degree of polymerization calculation mode, it can't give full play to the resources of the edge device such as computing, storage, etc. Fog computing can improve the resource utilization efficiency of the edge device, and solve the problem about service computing of the delay-sensitive applications. This paper researches on the framework of the fog computing, and adopts Cloud Atomization Technology to turn physical nodes in different levels into virtual machine nodes. On this basis, this paper uses the graph partitioning theory to build the fog computing's load balancing algorithm based on dynamic graph partitioning. The simulation results show that the framework of the fog computing after Cloud Atomization can build the system network flexibly, and dynamic load balancing mechanism can effectively configure system resources as well as reducing the consumption of node migration brought by system changes.
基金National Natural Science Foundation of China (Grant Nos. 11371355 and 11471193)
文摘Let G be a weighted hypergraph with edges of size i for i = 1, 2. Let wi denote the total weight of edges of size i and α be the maximum weight of an edge of size 1. We study the following partitioning problem of Bollob′as and Scott： Does there exist a bipartition such that each class meets edges of total weight at least （w_1-α）/2＋（2w_2）/3？ We provide an optimal bound for balanced bipartition of weighted hypergraphs, partially establishing this conjecture. For dense graphs, we also give a result for partitions into more than two classes.In particular, it is shown that any graph G with m edges has a partition V_1,..., V_k such that each vertex set meets at least（1-（1-1/k）~2）m ＋ o（m） edges, which answers a related question of Bollobás and Scott.
