Hi there!

First of all I want to say that I'm not a mathematician and hope I will make myself clear.

My problem is the following: I have a planar graph G which doesn't have any bridges. For that graph I want to find the set of all induced cycles. I researched a bit on the terminology and I think those are the correct terms for what I have and want to do. I'm wondering if the problem is really NP-Hard and if there's any heuristics that can help me find the problem. Besides the graph I have some more information about it that might help: some of the paths in the graph are actually 1 degree curves. Said in other way, I have a bunch of 1 degree lines that intersect with each other and I want to find all those "small and independent" loops they define.
Can anyone give me at least some clues/directions on where to get a good solution for it?