What is the expected run time (+/- a factor of 10) on a 486DX/50
using the best known algorithm for finding the shortest path
solution for Rubicks Cube from a randomly chosen position?

I have read the FAQ and followed the recent discussion on Rubicks
Cube but I don't believe this question has been answered.  Notice
that I am specifically looking for an algorithm that finds the 
SHORTEST path, not just any solution.

It seems to me that the underlying assumption is that such a program
would need to do a brute force search though 10^20 positions.  That
seems an unreasonably pessimistic assumption to me and I want to 
know if someone has significantly improved on that.

I have some ideas of my own on how to approach this problem, but
before I spend to much time developing them I wanted to know if
someone else has already done the work.

ADMINISTRIVIA:  I have posted this to three groups and attempted
to set the followup to rec.puzzles which seems to me to be the
place to continue this discussion.  I will cross post a summary
when and if it becomes appropriate.  Email replies gladly accepted.