There are many open source algorithms using visual SLAM. Use this link to check for a few implementation. I am not sure what you mean by applying it for cars, theoretically they should work if you are using stereo vision to get data, be it robots or cars.
I would suggest starting with ORB-SLAM, Open RatSLAM and OKVIS since they seem to provide better results in most cases. You can of course try other algorithms for comparing the performance. Some of the algorithms may be for monocular camera but later might release a version for stereo camera, so look out for that. Other algorithms that may be interesting based on your question would be LSD SLAM, LibViso, PTAM to list a few. You also mentioned finding some papers on the related topic, it is quite likely that they already have some kind of implementation in place to take a look at.
Also if you are looking for data with cars, KITTI dataset seems to be quite popular.
With my limited experience I would say there is not yet best algorithm which can be identified.
