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I'm looking for an algorithm that is faster than exponential which will find ANY cycle in a traveling salesman problem. It doesn't matter how bad the cycle is, it just needs to be a cycle. What I'm really looking for, then, is an algorithm for a hamiltonian circuit. Something that will start at a point, reach all other points, and then end at the starting point on a graph like this: http://neogen.amdusers.com/wikipics/projects/tsp.png

So far I have found this random algorithm which did not seem to work for my example case: http://www.princeton.edu/~achaney/tmve/wiki100k/docs/Hamiltonian_path_problem.html

And "Palmer's algorithm" which I'm having trouble understanding: Palmer's Algorithm for Hamiltonian cycles

Are there more than these 2 algorithms for doing this?

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  • [Angluin--Valiant](http://www.sciencedirect.com/science/article/pii/002200007990045X), which works with high probability for random graphs. – David Eisenstat Apr 20 '14 at 14:34
  • Palmer's algorithm is essentially 2-opt local search with 0-1 distances, so you can refer to the abundant materials on TSP 2-opt as well. – David Eisenstat Apr 20 '14 at 14:36

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