- The article describes various incorrect algorithms for loop detection in puzzle games, including the dangling-edge pruning method that highlighted too many edges
- The face-dsf algorithm worked perfectly for planar graphs but failed on toroidal surfaces due to nontrivial H1 homology, missing global loops
- The footpath-dsf algorithm fixed the torus issue but still had bugs with specific loop configurations on tori
- Tarjan's bridge-finding algorithm was ultimately adopted as it works on any graph without depending on topological embedding
- A corrected version of the loop-tracing algorithm could also work but is less efficient than Tarjan's approach