I'm looking for a fast suffix-array construction algorithm. I'm more interested in ease of implementation and raw speed than asymptotic complexity (I know that a suffix array can be constructed by means of a suffix tree in O(n) time, but that takes a lot of space; apparently other algorithms have bad worst-case big-O complexity, but run quite fast in practice). I don't mind algorithms that generate an LCP array as a by-product, since I need one anyway for my own purposes.
I found a taxonomy of various suffix array construction algorithms, but it's out of date. I've heard of SA-IS, qsufsort, and BPR, but I don't really know how they compare to each other, nor if there are even better algorithms. Considering how hot the suffix-array field seems to be right now, I expect that some other algorithms have superseded those since they were published. I seem to recall coming across a paper describing a fast algorithm called "split", but I can't find it now for the life of me.
So, what's the current state of the art? Ideally, I'd like a short list of the current best algorithms (with links, if possible) and a quick overview of their relative strengths and weaknesses.