# Finally getting somewhere (maybe)

For the last few days I’ve been fiddling around trying to get this library working. It supports LCA queries on suffix trees, which is quite nice. However, it’s been a bit of a pain to compile and it’s also written in C++ which I have no experience with and have to make work with my existing C code. Oh, and Valgrind doesn’t seem to like it too much (but only if I compile it; the examples compiled with the supplied Makefile run fine through Valgrind — odd) but I’ve emailed the developer about this.

But no matter, I think I’m getting there with actually performing LCE queries with it; certainly I’ve managed LCE queries on a few simple strings. A few bugs have come up trying to integrate it into the rest of my work, but lets hope (and pray) they’re easy to fix.

On a side note, I’m going to have to do a little more work on the rest of the $O(n \sqrt{k} \log{m})$ method anyway. I’ve been able to generate inputs that have the same text and pattern lengths and the same k but fall into different cases becase one has more frequent symbols than the other and, excluding pre-processing time, case 1 has been up to 10x as slow as case 2! Whether or not it’s worth trying to reduce the time complexity to $O(n \sqrt{k \log{k}})$ or it would be better to simply change the maximum number of frequent symbols allowed for case 1 to be used (I would assume that changing it from $2\sqrt{k}$ to some fraction of that wouldn’t affect the time complexity, but I’ll need to check) I don’t know.

Food for thought I guess.