I've spent a great deal of time over the last decade+ trying to find an efficient algorithm for NP hard problems and one thing I've learned is that this field is a graveyard for seemingly good ideas. Therefore I tend to be very skeptical of any paper that claims to solve such a problem but doesn't provide any empirical evidence that their solution works. I mean I've had hundreds of ideas and very few of them have survived without counterexamples appearing even for very small instance sizes.

I first saw this paper yesterday when it was posted on HN but didn't make it to the front page and I'm uncertain about how much energy to put into it (unfortunately my health gives me very little to spare). So far I've only read the introduction and it doesn't obviously involve any advanced mathematics that I'm unfamiliar with so I could perhaps attempt an implementation.

In addition to what I said above another factor arguing against investing much time in this is the fact that this was first published last year and nothing seems to have come of it in that time. Moreover it appears that the current paper is a revision from the one that was published last year. Does anyone know what the history of this was ? Were bugs found in the first version ?