Someone "reinvented" our algorithm, is there anything to do about that? A couple of years ago, we have published a paper in a reputable IEEE conference in field A. Recently (two years later), a paper in field B solved the same problem with the exact same algorithm without mentioning our work (the problem is of value to both fields).

We have tried contacting the authors but they do not respond. 

While I cannot know if they have seen our work or not, other works are already citing the new paper as the one that solved the problem (without mentioning us).

Is there anything we can do about this?
The place to start, if the authors don't respond, is to contact the editors of the journals that published both papers - or at least the editor of the other - pointing out the issue and giving references. 

Perhaps nothing improper has happened, but you can at least ask for a note/erratum posted with the other paper so that you get more visibility. 

I doubt that you can get more than that, but if you start there, at least, you can get proper recognition. 

Parallel work is pretty common. Not recognizing something similar if it appears in another field seems pretty natural. Maybe something worse, but hard to know. Contacting their editor may get them to contact you, one hopes. 

BTW, the reason for contacting your own editor is that they might also get involved in a solution.