# Getting caught in a loop while traversing a (directed acyclic) graph

How to detect if you are getting caught inside a loop when you are traversing a directed graph. This is equivalent of checking if you graph is a Directed Acyclic Graph (DAG).

Assume that each vertex of graph has a label such as A, B, C, etc. While you are traversing the graph, you keep your labels of traversed vertices on a stack or in a vector. If you construct a string out of this traversal, you will get a pattern like the following one.

` A,B,D,E,F,D,E,F,D,E,F`

Whenever you are caught in a loop, a path will repeat itself. We have D,E,F repeating itself. Now there are two ways to detect this. One is a classical graph based method which is efficient $O(E+V)$. The second one, about which I am going to talk about now, is not as efficient as first but but it is very easy to code. It is based on regular expressions.

All we have to do is  construct a string out of the data-structure which holds the vertex traversal order and match it against a regular-pattern which looks for the repeated substrings.

Here is one such pattern written using boost regex library.

` boost::regex rx ("^([0-9a-zA-Z_@]+,)+(?[0-9a-zA-Z@_,]+)(g{cycle})\$", boost::regex::perl);`

Care has to be taken while using this regex. First, I have special character @ in the label of vertex. And this pattern assumes that if there is a single repetition such as A,B,A,B or A,B,B etc, then it must lead to a loop. In my case it is justified. You should think if this is the behavior you want. And again, it is not as efficient as standard graph algorithms to detect loop (which uses Depth First Search). But for writing quick tests, it is a good approach.

I have used boost regex library. I am already using boost graph library therefore I need not look for other libraries. I have heard a some good things about GNU-regex library but have never used myself. Also, my gcc (4.6) does not support 2011C++ fully e.g. regex is not implemented fully. Have a look at its status page before writing any regex using header <regex>.

Dilawar