On 7/5/07, Jens Müller <jens.mueller@ira.uka.de> wrote:
Aaron Windsor wrote:
On 7/2/07, Jens Müller <jens.mueller@ira.uka.de> wrote:
Aaron Windsor wrote:
I've put two sets of files in the vault under Home/Algorithms/graph: the first is called planar_graphs.zip (also planar_graphs.tar.gz) and contains the .hpp files, the documentation, and the examples. The second is called planar_graph_testing.zip (also planar_graph_testing.tar.gz) and contains over 1000 test graphs and a small program that can be compiled to give an example of how these planar graph tools can be used. I'd appreciate any comments!
1. It would be nice if bidirectional graphs could be supported as well.
Hi Jens,
Thanks for taking a look at my implementation. Yes, it would be nice if bidirectional graphs were supported - they should be, and if it doesn't turn out to be too much trouble, I'd like to support them. I'll check on this when I have a little more time over the next couple of days.
IMO, the only difference between undirected and bidirectional graphs is (see http://www.boost.org/libs/graph/doc/graph_concepts.html#sec:undirected-graph...): that in bidirectional graphs, you have to iterate over in and out edges seperately. Even source(e) and target(e) are used the same ...
I'm not sure I understand your point on bidirectional graphs. bidirectional graphs offer the in_edges and in_degree functions, but for undirected graphs, these two functions will yield the same thing as out_edges and out_degree, respectively. So the distinction only really matters for directed graphs, right? In any event, I checked the implementation and updated the documentation of the Boyer-Myrvold planarity test so that it specifies that the algorithm requires an undirected graph that models both the IncidenceGraph and VertexAndEdgeListGraph concepts. Since BidirectionalGraph is a refinement of IncidenceGraph, it is supported. Am I still missing your point?
3. What is your implementation doing when the graph is not undirected or when there are self-loops?
It's undefined on anything that isn't an undirected graph with no self-loops and no parallel edges. The Boyer-Myrvold algorithm relies on several computations on an undirected DFS tree like lowpoint, least ancestor, and the full suite of planar testing/embedding/drawing algorithms rely on some algorithms that are only defined on undirected graphs, like testing simple connectivity and finding biconnected components. This is a case when it would be nice to have some adapters in the BGL to treat directed graphs as undirected or vise-versa.
You mean bidirectional graphs ;-) Yes, that would be nice, and not that very much complicated, I suppose. I just replied to a post by Benoit from November 2006 who asked for a bidirectional->undirected adapter as well. Maybe my bidirectional->"bidirected" adapter can serve as a starting point, which is in turn based on the graph reversal adapter by David Abrahams.
When I now think of it, I wonder wether it would have been feasible to use a undirected graph for this - I suppose yes ... Probably my design choice was due to the original LEDA-based implementation I'm working with, which called G.make_bidirected(). Gotta take a look on it.
That, of course, does not solve the problem with self-loops and parallel edges. IMO, it should be possible to construct planar embeddings for graphs containing them, as well. Maybe deleting them from the graph first and later "multiplying" edges again? This would mean adding them in opposite order in the adjacency lists of the two end-point nodes, I suppose.
Do you know which steps of the algorithm rely on there being no self-loops or parallel edges?
I modified the implementation so that everything works correctly in the presence of self-loops and multiple edges. I just uploaded the latest source to the vault, so give it a try if you're interested (http://tinyurl.com/2dltju). All of the algorithms: planarity testing/embedding, kuratowski subgraph isolation, the planar face traversal, and straight line drawing now handle parallel edges and self-loops. Please let me know how it works for you. Regards, Aaron