Theorem 1(Erdos)Every graph G has a spanning bipartite subgraph G′ ,where every vertex of G′ satisfy dG′(x)≥12d(x),dG′(x) means the degree of x in subgraph G′ 我们可以给出两种证明,一种依赖于概率,一种是通过算法(?)比较得出的 不妨设 G′=A∪B First proof: 对于一个点 v...
Loop-erased partitioning of a graph: mean-field analysisAlexandre GaudilliereLuca AvenaMatteo QuattropaniPaolo Milanesi
Let a k-partition of a graph be a division of the vertices into k disjoint subsets containing m1 ≥ m2, …, ≥ mk vertices. Let Ec be the number of edges whose two vertices belong to different subsets. Let λ1 ≥λ2, …, ≥λk be the k largest eigenvalues of a matrix, which is...
Partitioning a graph in O(¦A¦log2¦V¦) We present an algorithm to partition a graph, where V is the set of vertices and A the set of arcs, extending Hopcroft's fast partitioning algorithm. A Cardon,M Crochemore - 《Theoretical Computer Science》 被引量: 85发表: 1982年...
Graph similarity computation, which predicts a similarity score between one pair of graphs, has been widely used in various fields, such as recommendation system [42], [16], computer vision [15], [35] and so on. However, most of the standard distance measures evaluating how similar two grap...
3.A part or section into which something has been divided. 4.Division of a country into separate, autonomous nations. 5.Mathematics a.An expression of a positive integer as a sum of positive integers. b.The decomposition of a set into a family of disjoint sets. ...
Traditional graph partitioning algorithms compute a k -way partitioning of a graph such that the number of edges that are cut by the partitioning is minimi... G Karypis,V Kumar - IEEE/ACM Conference on Supercomputing 被引量: 848发表: 2005年 Parallel Multilevel Algorithms for Multi-constraint ...
Distributed graph computation is central to applications ranging from language processing to social networks. However, natural graphs tend to have skewed power-law distributions where a small subset of the vertices have a large number of neighbors. Existing graph-parallel systems suffer from load imbala...
of a graph such that certain objective is met, e.g., it is possible to seek partitions into a given number of equal-sized sets such that the number of edges having endvertices in distinct sets is minimized or, as in this paper, one can minimize the number of the resulting sets under...
International Journal of Foundations of Computer ScienceM. Holzrichter and S. Oliveira. A graph basedD avidson algorithm for the graph partitioning problem. International Journal of Foundations of Computer Science , 10:225–246, 1999. 705, 709 MathSciNet...