I think there are multiple algorithms supported because none of the algorithms are clearly the best choice in all cases.
The differences are in readability of the patch output and processing time needed to generate the patch.
Summarizing, this is what I understand the differences are:
- Myers: The original algorithm as implemented in xdiff (http://www.xmailserver.org/xdiff-lib.html and http://www.xmailserver.org/diff2.pdf), optimizing the ‘edit distance’ for changed lines.
- Minimal: Myers plus trying to minimize the patch size.
- Patience: Attempts to trade readability of the patch versus patch size and processing time. See What is `git diff –patience` for? and http://bramcohen.livejournal.com/73318.html or http://alfedenzo.livejournal.com/170301.html for a description.
- Histogram: Mainly created for speed. Faster than Myers and Patience, originally developed in jgit (http://eclipse.org/jgit/)
Here is a comparison of speed for Myers, patience, and histogram: http://marc.info/?l=git&m=133103975225142&w=2
Here is a comparison of diff output of Histogram vs Myers: http://marc.info/?l=git&m=138023003519837&w=2