I have found a polynomial time solution of an NPC problem. My algorithm give exact result in most cases. For example if I run my algorithm for 20000 problem instances, then it fails 10 times to give correct result. But, I am unable to prove the approximation ratio mathematically. Is it feasible to show it with the experimental results? I am waiting to hear the possible solutions for it.
First of all, any more information to give about the problem? Your algorithm? These sorts of things would make a question such as this far more approachable.
In what sense are you unable to prove it? I think a theoretical result is far stronger than any experimental results you may be able to gather, since it demonstrates that, without fail, your algorithm will return a solution with a value within some constant factor of the optimal for any given instance of the problem. The instances of the problem that your algorithm fails to give a answer for, do you notice any trends in terms of how 'off' the results are?