First thing first - I am not a CS guy. I am EE student (Systems and Signals). So it would help if you didn't use any big words :)
The Multi-terminal cut the input is a graph G and a subset T of its vertices. The task is to remove the minimum number of edges from G such that there is no path connecting any distinct vertices of T. Dalhaus et all showed that its NP-Hard for $k\ge 3$ for arbitrary.
Question - Why is this class of problem important? Do they show up in some engineering application.
A few years ago I found a simple algorithm proposed as an approximation of the Multi-terminal cut problem for arbitrary weighted slow-coherent graphs. (Strong connected components which are weakly connected with each other). I did a performance analysis of the algorithm from a linear algebra point of view and was able show that algorithm should be work for these classes of graphs.
I would like to take the algorithm and apply it to an application area and see how it fares compared to the "standard".