Firstly I wanted to ask. If I have a undirected graph and split all the edges into two directed edges is it still called directed or does it become bi-directed?
The main question is i have a graph with n sources all in the same graph until now I thought I could use the mssp method provided by Klein in this paper but it says that the graph must be a directed graph. Yet if I have an undirected graph and split each edges into two components with same weight I don't think it will be able to solve the problem or it does not matter?
Due the bidirection of the graph, will it have the first source visit each and every node without the other sources implying that I can't adapt the graph such that I can have a Shortest path tree as if I ran a dijkstra on the other sources does it?
Also I wanted to make sure does this method gets all the shortest path trees? because i was getting confused.
Klein algorithm is able to compute all the shortest path trees for specific starting nodes found on a single face (lets agree on that). Its secret is that it will do adaptations of specific darts found in the dual graph. if it is an undirected graph turning it into directed graph will become a bi directed graph by the following: can you still state that such graph is directed and also bi directed?
A directed graph is called bi-directed if the there is a mapping reversal() that maps each edge e=(v,w) to a reversal edge (denoted as reversal(e)) such that the following holds:
reversal(e)=(w,v), that is, the reversal edge of e indeed is reversely directed, so reversal() deserves its name. reversal(reversal(e))=e, that is, also in the presence of multiedges always two edges correspond to one another. e is different from reversal(e), that is, also in the presence of self-loops each self-loop edge has a different self-loop edge as its reversal edge. (don't have self loops)
Each edge e occurs as the reversal edge reversal(e') of a different edge e', that is, the mapping is bijective.
would you still be able to state that a I directed graph is also a directed graph?