Stabilization of maximal metric trees

We present a formal definition of routing metrics and provide the necessary and sufficient conditions for a routing metric to be optimizable along a tree. Based upon these conditions, we present a generalization of the shortest path tree which we call the "maximal metric tree". We present a stabilizing protocol for constructing maximal metric trees. Our protocol demonstrates that the distance-vector routing paradigm may be extended to any metric that is optimizable along a tree and in a self-stabilizing manner. Examples of minimal metric trees include shortest path trees (distance vector), depth first search trees, maximum flow trees, and reliability trees.