Shortest cycle with a specific number of vertices Given an undirected graph with n nodes, I need to find the shortest cycle of involving exactly n/2 vertices (i.e. keeping the distance traveled by the cycle to a minimum). Some nodes cannot directly connect; they're in specific areas and I can only travel from one area to another, not within one area.

I'm just asking in general here, what kind of techniques can I use to get the best (shortest) possible cycle of n/2 nodes?  So far I've written a basic substitution optimizer and just a greedy Depth First Search.  I'm wondering what would be the best approach for me to start on now?
The problem of finding the shortest tour that covers a given number k of nodes is usually referred to as k-TSP. Searching Google scholar for that term will find some relevant literature. It is NP-hard but can be approximated within a constant factor. So finding an exact solution may be out of reach, unless you're prepared to use sophisticated branch and bound methods extending what Concorde does for the usual TSP.