Shortest route with no set destination in Google Maps V3?

Question

So I'm just learning javascript to mess with the Google Maps API. I was wondering if anyone had an elegant solution to this problem I'm running into.

A Google Maps route request must contain three things (origin, destination, and travelMode). My travelMode will always be DRIVING. The origin will always be wherever the user is located.

The destination though, needs to vary. I have several waypoints and the user will visit, and would like to provide the shortest trip possible depending on what waypoints are selected and where the user is, ending the route at one of the waypoints (eg: ABC or ACB, but always Axx...x).

Is there any possible way to do this other than calculating every possible path and seeing which has the shortest distance (or time, or whatever I'm evaluating on)? It seems like that would be prohibitively costly (O(n!)).

edit: With the suggested optimizeWaypoints flag set to true this becomes a O(n) problem instead of O(n!), but now I have issues with issuing too many requests in too short of a time period.

Answer 1

http://en.wikipedia.org/wiki/Travelling_salesman_problem

Answer 2

There is a setting in google directions to provide optimized route (optimizeWaypoints - http://code.google.com/apis/maps/documentation/javascript/services.html#Directions ) you simply set it to true in your directions object