Inversion of algorithms is exactly what its name suggests: take an algorithm A and produce a new algorithm A' that undoes the job of A. This has been studied in many areas, but we are particularly interested in applications to computational biology.
The idea is basically to model a biological process as an algorithm, and then its inverse will solve relevant problems. For instance, if we model the process of shotgun sequencing as an algorithm, its inverse will solve the fragment assembly problem. If we model genome evolution, its inverse will solve genome comparison. And so on.
Here are some of our papers on the subject: