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在MapReduce中完成二部图

[英]Complete bipartite graph in MapReduce

原文 2013-12-23 11:53:17 1 1 algorithm/ graph/ mapreduce/ complete/ bipartite

I'm working on my degree thesis and I've been asked to write an algorithm to determine whether an undirected graph is bipartite and complete (ie there exist two disjoint sets of nodes such that every node of the first set is connected to every node of the second set and there is no edge connecting nodes of the same set) using MapReduce model. 我正在研究学位论文，并且被要求编写一种算法来确定无向图是否是二部图和完整图（即，存在两个不相交的节点集，使得第一个节点的每个节点都连接到每个节点使用MapReduce模型时，没有第二个集合的边连接，并且没有边缘连接相同集合的节点）。

Is triangles counting a good way? 三角形算是个好方法吗？

It has been proved by the Turán's theorem that a complete bipartite graph is a triangle-free graph with the maximum number of edges. 图兰定理已经证明，完整的二部图是具有最大边数的无三角形图。 So could it be a good way trying to modify the MapReduce NodeIterator++ algorithm described by Suri and Vassilvitskii in this paper (sections 3.1-4.1)? 因此，尝试修改Suri和Vassilvitskii在本文中描述的MapReduce NodeIterator++算法（第3.1-4.1节）是否是一个好方法？ My advisor told me to focus on this algorithm to solve this problem. 我的顾问告诉我专注于此算法来解决此问题。 This is attractive because this algorithm is optimal in terms of space and time complexity. 这是有吸引力的，因为该算法在空间和时间复杂度方面是最佳的。

Actually I'd like to achieve a more complex result 其实我想取得更复杂的结果

I would like not only to determine whether the graph is bipartite and complete but also to try to find the two disjoint sets of node which form the set partition. 我不仅要确定图是否是二部图和完整图，还要尝试查找形成集合分区的两个不相交的节点集。 This is surely going to take more MapReduce rounds but it's not a problem. 这肯定会花费更多的MapReduce回合，但这不是问题。

I need your help please. 我需要你的帮助。 Some hint and/or result that will drive me to the solution is well-accepted. 会促使我寻求解决方案的一些提示和/或结果是公认的。