This question concerns _[right angled Artin groups][1]_ (RAAGs), also called _partially commutative groups_ or _graph groups_.

A student of mine, Adi Ben-Zvi, needs for an algorithm in RAAGs, a subalgorithm that we suspect should be known. 

In RAAGs, it is known how to compute efficiently the centralizer of a single element [A Baudisch, Subgroups of semifree groups, Acta Math. Acad. Sci. Hungar. 38 (1981) 19–28; H Servatius, Automorphisms of Graph Groups, J. Algebra 126 (1987) 34–60]. In these papers, the cyclically reduced case is treated, but this obviously implies - since we consider a *single* element - the case of a general element.

**Question:**
Is there an efficient algorithm for computing, in RAAGs, the centralizer 
of a given finite set of (general) group elements?

We have a positive answer for sets of *cyclically reduced* elements, but thus far we only have special cases of the general case.

If no such algorithm is known, we would appreciate even results providing
information about centralizers of given finite sets.




  [1]: https://en.wikipedia.org/wiki/Artin_group