How to impose node balance ( as opposed to element balance)

we are using Parmetis 3.2 and running on some issues.
Parmetis works quite well and balances perfectly the number of elements per partition.
However the number of corresponding nodes is quite inbalanced. Mostly we believe it comes from the non connex partitions and the way our dual mesh was numbered ( we use the Parmetis routine to generate the dual mesh by the way).
This is a major issue for us since a lot of operations are node based.

I was wondering if there is a way to stronly encourage Parmetis to provide connex partitions and balance the number of nodes per domain a little more ( variability is 20%).


RE: ParMetis right now cannot

ParMetis right now cannot simultaneously balance elements and nodes. However, is there a way you can assign weights on the vertices of the dual mesh so that it will lead to a better node balance? For instance, you can potentially treat it as a multi-constraint partitioning problem, where the first weight is 1 to reflect the element balance, and the second weight is derived from the membership of the element's nodes in different elements. For example, if a node i belongs to ni elements, and i, j, k, l are the nodes of an element, how about using a weight of 1/(ni+nj+nk+nl)? [of course you will need to scale those to be integers].