The Algorithms Of Bipolar Orientations

Bipolar orientations not only have a wide range of applications in VLSI design and other engineering calculations, but also the basis of many drawing algorithms. So more attention has been paid in recent years.The concept of bipolar orientation was first introduced by Brooks,Smith,Stone and Tutte, as a purely mathematical treatment in 1940. In 1967, A.Lempel and S.Even proposed the concept of st-numberings in an article about planarity testing. In 1976 Even and Tarjan proposed an algorithm that computes an st-numbering of an undirected bi-connected graph in linear time. Since then, the bipolar orientation was widely used in VLSI design and graph drawing algorithms such as visibility representations, hierarchical drawings and orthogonal drawings.Based on the analysis of the fundamental circuit of a graph, this thesis shows two basic configurations of a circuit. By the optimization of these two configurations, an algorithm of the bipolar orientation is given.There are four chapters in this thesis:The first chapter introduces some basic concepts and their background.The second chapter shows two algorithms of the bipolar orientation, and gives a specific example each.In the third Chapter, we analyzed the fundamental circuit of a graph according to the absorption rule shown in, and proposed a new algorithm of the bipolar orientation.The fourth chapter gives a conclusion of the whole article and list some problem need further study.