skaller wrote:
> Does anyone know how to solve the parallel assignment problem
 > I seek a solution which minimises the number of assignments.

What, in polynomial time?

Most of the results seem to require paid subscriptions or a library at hand:
http://www.google.com/search?q=%22parallel+assignment+problem%22

But the comp.compilers link seems relevant and points further to

[3] Robert G Burger, Oscar Waddell, and R. Kent Dybvig.
           Register allocation using lazy saves, eager restores,
           and greedy shuffling. In 1995 ACM Conference on Programming
           Language Design and Implementation, June 1995, pages 130-138.
           Available online via
ftp://ftp.cs.indiana.edu/pub/scheme-repository/doc/pubs/Reg-Alloc-PLDI95.ps.gz

which claims NP-completeness for the problem.

Yours, Florian.