定向混合图的改进逼近
Improved Approximation for Orienting Mixed Graphs
摘要：
最大混合图定向问题的一个实例由混合图和源-目标顶点对的集合组成。该问题的目标是使图的无向边定向，以使允许有向源-目标路径的对的数目最大化，这个问题最近在生物网络的研究中出现，在通信网络中也有应用。在本文中，我们确定了一个有趣的本地到全球的方向属性。这一性质使我们能够修改最著名的算法最大混合图的方向和它的一些特殊的结构化的情况下，由于Elberfeld等人。（CPM '11），并获得改进的近似比。我们进一步进行开发的算法，实现了更好的近似保证的一般设置的问题。最后，我们研究了这个方向问题的几个动机良好的变体。
英文摘要：
An instance of the maximum mixed graph orientation problem consists of a mixed graph and a collection of source-target vertex pairs. The objective is to orient the undirected edges of the graph so as to maximize the number of pairs that admit a directed source-target path. This problem has recently arisen in the study of biological networks, and it also has applications in communication networks. In this paper, we identify an interesting local-to-global orientation property. This property enables us to modify the best known algorithms for maximum mixed graph orientation and some of its special structured instances, due to Elberfeld et al. (CPM '11), and obtain improved approximation ratios. We further proceed by developing an algorithm that achieves an even better approximation guarantee for the general setting of the problem. Finally, we study several well-motivated variants of this orientation problem.
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