Maximizable routing metrics

We develop a theory for deciding, for any routing metric and any network, whether the messages in this network can be routed along paths whose metric values are maximum. In order for the messages in a network to be routed along paths whose metric values are maximum, the network needs to have a rooted spanning tree that is maximal with respect to the routing metric. We identify two important properties of routing metrics: boundedness and monotonicity, and show that these two properties are both necessary and sufficient to ensure that any network has a maximal tree with respect to any (bounded and monotonic) metric. We also discuss how to combine two (or more) routing metrics into a single composite metric such that if the original metrics are bounded and monotonic, then the composite metric is bounded and monotonic. Finally we show that the composite routing metrics used in IGRP (inter-gateway routing protocol) and EIGRP (enhanced IGRP) are bounded but not monotonic