An Efficient Algrithm To Find All 'Bidirectional' Edges Of An Undirected Graph

An efficient algorithm for the All-Bidirectional-Edges Problem is presented. The All-Bidirectional-Edges Problem is to find an edge-labelling of an undirected network, G = (V,E), with a source and a sink, such that an edge [u,v] /spl epsi/ E is labelled (u,v) or (v,u) (or both) depending on the existence of a (simple) path from the source to sink that visits the vertices u and v, in the order u,v or v,u, respectively. The algorithm presented works by partitioning the graph into a set of bridges and analyzing them recursively. The time complexity of the algorithm is shown to be O(\E\ . \V\). The problem arises naturally in the context of the simulation of in MOS transistor network, in which a transistor may operate as a unilateral or a bilateral device, depending on the voltages at its source and drain nodes. For efficient simulation, it is required to detect the set of transistors that may operate as bilateral devices. Also, this algorithm can be used in order to detect all the sneak paths in a network of pass transistor.