It is critical to understand that this article fundamentally misuses the word "homology", which in bioinformatics and molecular evolution is understood to mean "sharing a common ancestor". Similarity searches (typically using programs like BLAST, one of the most cited methods in the biomedical literature) look for homologs.
This article is NOT about "homology" detection (which suffix trees are not particularly good for), it is about "identity" detection (which is a related problem, but fundamentally different). It is unfortunate that in the biomedical literature, the word "homology" is often misused in place of "identity" (as in "micro-homology", which is really "micro-identity"), but serious computational biologists try to avoid this misuse of the word "homology".